Your lens is almost the only important aspect of this technique, but before I get into that I need to mention a couple other things...
Since you need to be able to choose your lens - an interchangeable lens compact (ILC) is a minimum requirement for the technique.
A full frame sensor is ideal here. Although using the same lens on a smaller sensor camera technically has the same potential it will require you to shoot more images to reach the same result (2.25x as many images for APS-C and 4.5x for M4/3). Here are a few pros and cons to using smaller than full frame sensor cameras for this technique:
Higher quality parts of the optics (sharper images)
Less aberrations (CA, vignetting & mechanical vignetting)
Higher resolution (generally)
Missed moments & dwindling interest - due to exponentially time consuming workflow
Increased overlap issues - resulting in a failed stitch and/or stitching errors
Memory issues - camera buffer & computer RAM running out
Processing - workflow speed
Larger than full frame (Medium Format) cameras are not ideal for this technique because their lenses are not as fast. You can adapt some full frame lenses to medium format cameras like the Fuji GFX and have them project over the whole sensor. This looks great for single images, but would not be great for this technique due to corner performance being unintentional (bad quality).
Choosing A Lens
Maximizing this technique's effect requires a large aperture (which can be worked out by dividing a lens's focal length by its f-stop). A 50mm f/1.0 and a 100mm f/2.0 both have the same 50mm aperture size. Double the focal length will require you to take four times as many images to reach the same result, however. Ignoring the cost, for now, longer focal lengths almost always have higher image quality, but they are harder to use (also because they are heavier). Balancing aperture size and focal length for effect vs workflow can be tricky, so I made this graph (below) to help visualise usability when choosing a lens for this technique.
Using The Chart
First look for a focal length (top bar), follow the dotted line down to where it intersects an f-stop value, then follow that point to the left to see the physical aperture size (bigger = better). The main purpose of this chart is to balance workflow complexity with potential subject isolation.
The bottom numbers in this chart tell you how many images you'll need to shoot when emulating a 28mm wide-angle (after cropping) from each focal length. With equivalents for each sensor size it also illustrates how much easier full frame is to use for each focal length, by requiring so fewer images.
If you don't need to emulate a lens this wide then the chart is not so useful, then the longer focal length lenses need not be so harshly punished or omitted entirely. You may shoot a 200mm f/2.0 and only want to emulate a 100mm f/1.0, which would require shooting only 9 images. This would be pretty easy despite the lenses extreme weight and size (relative).
Weight is something that is not taken into account here, although it will greatly affect your ability and patience to shoot many images (at least hand-held). That said - the lenses weight generally increases when the focal length and aperture size is increased, so lenses towards the top right of this chart are generally more heavy. To see more info on this scroll down to the next graphs.
This chart also does not take price into account. That might seem like a shame, but trying to relate a specific aperture size against cost can be extremely complicated, especially if you're going to factor in manual focus and vintage lenses. This is something that I will try to cover in this section however, so please see the 'Budget Lenses' section below for more info.
If you're looking for the best lenses for the Bokeh Pano technique in this chart you will find them in the top left corner.
Chasing Big Apertures
These are some of the lenses that I have used to shoot Bokeh Panos in my pursuit of the best effect. These are all primes with large aperture sizes. They are (clockwise from top):
Sigma 135mm f/1.8 Art - 75mm aperture
Canon FD 135mm f/2 - 67.5mm aperture
Canon FD 85mm f/1.2 - 71mm aperture
Even larger aperture lenses do exist, for example:
75mm f/0.95 - 79mm aperture
135mm f/1.4 - 96mm aperture
200mm f/2 - 100mm aperture
300mm f/2.8 - 107mm aperture
400mm f/3.5 - 114mm aperture
250mm f/2 - 125mm aperture (rare, old Olympus lens)
350mm f/2.8 - 125mm aperture (rare, old Olympus lens)
400mm f/2.8 - 142mm aperture
300mm f/2 - 150mm aperture (rare old Nikkor lens)
500mm f/2.8 - 178mm aperture (Sigma 200-500 Zoom)
When not emulating wide results then these lenses are as amazing as they sound. Using them to make a 20-40mm field of view in your final stitch, however, would require shooting hundreds of images. These lenses also get exponentially heavier too, so hand holding them for this many images would be tough. Let me try to quantify this...
Size Isn't Everything
This more simple list orders lenses by sheer aperture size, left to right. The first one is the best smartphone currently on the market... just for comparisons sake.
This first chart (above) shows a bunch of lenses commonly used for shooting Bokeh Panos (accept the first one). All the charts you will see below are in the same order as this (further right = bigger aperture).
This chart shows how the heavy the lenses with the largest apertures get, making them difficult to hold long periods. Since they also require exponentially more images to get wide angle results you won't be able to use them in that way.
Note: The Sigma 105mm f/1.4 lens, which I mentioned in the best lenses ever section, is not listed here. The one shown is the Nikon version. The sigma would be getting red and thus showing it as a negative here. At 1.6Kg it weighs a lot for a 105mm lens (twice that of the Canon EF 24-70mm f/2.8 II lens, which itself is no feather-weight).
The Meyer Optik 75mm f/0.95 is the stand-out winner here. For such a large aperture it's tremendously light weight. Unfortunately this lens was planned, but is no longer (due to the demise of Meyer Optik). We can't be sure that this ever would have been possible, but if it was it would have been amazing!
This chart shows which lenses are easier to use due to requiring less shots to achieve a given result. These values are from shooting on a Full Frame camera. If shooting on an APS-C then you would have to times the values by 2.25, if shooting on a M4/3 camera then times the values by 4.5.
Apex Of Perfection
These are THE best lenses for Bokeh Panos regardless of cost. Of course this is subjective and although not based on practical experience these are rated on several factors (aperture size, image quality, mechanical vignetting, focal length, size / weight). Autofocus speed, or even whether it focuses automatically at all is not considered because focus is locked while shooting anyway.
1. Nikkor AFS 105mm f/1.4E ED - (75mm aperture) - 985g / $2200 [F]
The original 105/1.4 lens design is still a stunning one. It isn't cheap, but then none are and this one is relatively small and light for what it is.
2. Sony G Master 135mm f/1.8 - (75mm aperture) - 950g / $2000 [FE]
This new lens manages to improve on the stunning Sigma Art lens for sharpness and AF speed / accuracy, while being significantly smaller & lighter. Of course it's more expensive, but if you have a Sony A7 or A9 it looks like it's worth it.
3. Sigma ART 105mm f/1.4 DG HSM - (75mm aperture) - 1640g / $1600 [F, EF, FE, SA]
Knocked down to the number 3 spot due to be insanely big and heavy, while not fixing the dreaded mechanical vignetting issue.
4. Any 75mm f/0.95 - (79mm aperture) - ?g / $4000? [FE, Z, RF, L]
If this lens ever ends up actually getting made it could easily make it to the top spot. Original vapourware for this was announced by Meyer, but then NISI actually made a sample that people tested. The latest rumour is that a 'Rumiere' branded lens could appear first and might be made by the same company that makes Mitakon lenses.
5. Canon EF 200mm f/1.8 - (111mm aperture) - 3000g / $2500 (SH) [EF]
This discontinued lens could easily be considered the best for this technique. Like it's slightly slower brother (200/2), if you don't need to emulate a wide lenses, or are happy shooting a ton of frames on a tripod it's sheer epicness! Shooting only 9 images on a full frame camera will get you a 100mm f/0.9 equivalent!!
6. Sigma ART 135mm f/1.8 - (75mm aperture) - 1030g / $1400 [F, EF, FE, SA]
This requires a few more images than the 105mm f/1.4, but it has just as good image quality and bokeh amount in a smaller and lighter package. This is the only lens in this list that I actually own so the rest are purely here for their aspirational technical specs. The edge to edge performance of this lens is stellar!
7. Mitakon Speedmaster 135mm f/1.4 - (96mm aperture) - 3000g / $3000 [FE]
Only a handful of these elusive monsters will be made. Although the focal length is a little on the long side, the bigger problem here is its weight. Using it handheld for wider results is all-but off the table, but it deserves a special mention here due to that epic aperture size (for a lens of this focal length), which can't be understated. Try finding sample images of actual bokeh from this lens is pretty much impossible so I wonder if anyone actually owns one. For this reason (and physics) I will assume that mechanical vignetting is also not great here, like the Nikon 105mm (above).
8. Canon EF 85mm f/1.2 L - (71mm aperture) - 1025g / $1600 [EF]
This AF version of the original Canon 85L (below list) is significantly bigger, heavier and more expensive. It might surprise you to know that it doesn't improve on the image quality much (if at all), but it does give you autofocus and works on Canon DSLRs much more easily. It's still a great lens for shooting Bokeh Panos, but just not quite as neat or as reasonably priced as it's older brother.
As you can see above - large aperture lenses tend to be expensive, so here are a few tips to find some relative bargains for this technique. Firstly I recommend looking for manual focus lenses. New brands like Samyang or Mitakon offer great value for money and support most DSLRs.
Older manual focus lenses are also a great option, but check carefully as to whether your camera's lens mount can take them. Mirrorless has a big advantage here because they can adapt cheaply to many (possibly all) of the old SLR mounts and this will be where the best bargains are to be had. Sony is currently the best option of the mirrorless systems because they have the biggest support for other mounts (especially with autofocus), but also because they are the only one with a full frame option (Although Nikon and Canon are not too far off now, after 5 years) - the original A7 is also great value now (especially second hand).
There are lots of great old manual lenses. You can spend weeks looking through Ebay at: Nikon, Olympus, Pentax, Canon, Minolta, Yashica, Konica etc. As well as Russian M42 mount lenses from Helios, Jupiter and many others.
Digital SLRs have a much more spotty support for old lenses. Although Canon's EOS mount has a shorter flange distance, giving it greater support various mounts (it can use Nikon F, Pentax K and M42 lenses for example). Oddly the Canon EOS mount can't take their own legacy FD lenses without using extra optics or being expensively converted. This is a big shame because there are many awesome bargain FD lenses to be had. Mirrorless cameras like the Sony A7 can adapt to them easily and cheaply however.
For those of you on a lower budget, fear not! There are some great options. Some of the options below offer aperture sizes to rival the the 'apex' crowd and some even have autofocus (althoguh usually not both). Much of this is either vintage or Chinese. The former often have great build quality, characterful rendering and beautiful focusing, whereas the latter can offer very impressive image quality and sometimes autofocus.
(48mm aperture) 135mm f/2.8 Various - 400g
(28mm aperture) 50mm f/1.8 Various - 200g
(54mm aperture) 135mm f/2.5 Various - 500g
(47mm aperture) 85mm f/1.8 Kelda - 400g [EF]
(42mm aperture) 85mm f/2 Jupiter - 320g [M42]
(42mm aperture) 105mm f/2.5 Minolta - 375g [MD]
(50mm aperture) 100mm f/2 Yongnuo - 440g [EF]
(47mm aperture) 85mm f/1.8 Various - 400g
(42mm aperture) 105mm f/2.5 Nikkor - 435g [F]
(75mm aperture) 135mm f/1.8 Porst - 800g [M42]
(61mm aperture) 85mm f/1.4 Samyang - 540g [F, EF, FE, PK]
(58mm aperture) 105mm f/1.8 Nikkor - 580g [F]
(45mm aperture) 50mm f/1.1 7 Artisans - 400g [M]
There are a few lenses that I have chosen and would probably choose them again regardless of cost. This is usually because they represent a great balance of aperture size vs weight (+ physical size). The ideal being the smallest lens that can provide the greatest effect.
Canon FD 85mm f/1.2 L - (71mm aperture) - 660g / $600 (SH) [FD]
I keep coming back to this lens to shoot Bokeh Panos because it's relatively small & lightweight considering its aperture. It's strange because this doesn't easily fit into either of the above categories (almost Apex, but not Budget). For what it is the effect is amazing, image quality if surprisingly good, the focus mechanism is gorgeous and the balance / build on the newer Sony A7III (below) feels great - like a mini tank.
Mitakon Speedmaster 50mm f/0.95 - (53mm aperture) - 700g / $750 (New) [FE]
By far the cheapest 50mm lens this fast. If you own a Sony A7 and are reading this then you like shallow depth of field and I highly recommend that you look into this lens. It doesn't have the largest aperture, nor is it the cheapest, but it is one of the easiest to use that provides a very decent effect.