I have an older (~'73) campy pista crankset, but no bottom bracket. Do I have to find an older campy bottom bracket, or will a newer one fit the same? Are there other modern (or older) cheaper brands that would work, such as miche? Or is the spindle taper specific to campy?

Miche will work. I have used them for old T.A. and Campy Record.

Don't tell anyone but just to get my Pog on the track I used a Miche BB and Sugino Pista crankset. . .

Another option is a Phil BB.

Marty

I don't know the answer to your question, but I suspect that a new BB will work fine because - I have a 73 Campy pista BB and I'm pretty sure the spindle is symmetric, whereas the double at the time had an asymmetric spindle that was longer on the drive side. I also have a late 80's Athena BB for a double and the spindle is symmetric. So you need to find out if there is an issue with the tapers on a new BB and how long the spindle needs to be so that the crank does not interfere with the chain stay. I'm guessing that a new Miche pista BB will work fine because the cartridge position in the frame BB is adjustable. Others here are likely to know.

What length miche would I need? My rear spacing is 120 and I have standard track wheels/42mm chainline.
I do have an 111mm campy BB for a double, would that throw my chainline too far off? I'm leaning towards the adjustable miche...

Modern (last 5 years or so) Campy triple sealed cartridge BB is symetrical and 111mm (same as old Record Pista). Veloce and lower models can be had cheap online. The taper is technically different but in my opinion not enough to cause any problems. I've done it a few times and it's worked fine giving a straight chainline to a 120mm track hub.

I noticed on businesscycles they sell a modern record pista BB @ 111mm, and a record pista #1046 (cup and cone) @ 109mm. So now I'm thoroughly confused!

The adjustability of the Miche is nice. You can get the chainline perfect. The Phil has the same feature for 500% more.

What spindle length miche would I need, 107 or 110?

Well after reading numerous complaints about miche bottom brackets working loose I am hesitant to go that route. I'll see what my LBS suggests...

According to this:https://www.campyonly.com/history/1974/chainlines.pdf
There is a 1mm difference between a 68-SS-120 chainline, and a 68-P-120 chainline.
I have the 68-SS-120 bottom bracket. So the question now is, where would a pista chainring line up on the spindle, closer to the inner or outer chainring?

The SS-120 is asymetrical so you'll have 2 choices by flipping it

Again I would suggest using a Veloce or lower model triple at 111. Done it a few times with good results.

I ended up using my old 68-SS-120 campy BB, 111mm spindle. Chainline was ~43mm up front, and ~43 rear with the addition of a 0.5mm spacer behind the cog. I haven't ridden it yet but hopefully it will be smooth sailing!

Also, the chainring cleared the chainstay by only ~2mm, cutting it kind of close!

I haven't had a problem with the Miche bb working loose, but I can see how it could happen if the rings aren't torqued enough. It could also happen to a Phil. The 110mm Miche would have worked.

The .5mm spacer won't be a problem.