I bought a 1984 Trek 400 frame that I'm looking to convert to a singlespeed. I was looking at cranksets and am confused over the types I can get based on the BB. So basically, what BB size(s) would be compatible with the Trek so I know which crank set to get?

It uses an English threaded bb, 68mm wide.
If you are looking for a crankset, Eighthinch crankset is very good choice for $50.
https://www.cyclingcloseouts.com/Prod..._Crankset.aspx
Here's the bottom bracket to go with it.
https://www.universalcycles.com/shopping/cart_view.php

Thanks so much for the info! The link for the bottom bracket didn't work. Can you repost that? Also, does the length of the bottom bracket matter?

The spindle length matters because you will need the straightest chainline; a bottom bracket too short or too long would not make your chainline straight.
https://www.universalcycles.com/shopp...s.php?id=14284
Pick the one that says 68x107mm, basically the first one.
The crankset requires a 103mm long spinde, a 107 would work fine but you'd have to put the chain ring on the inside of the cranks. If you want to have the chain ring on the outside and don't mind paying extra $10 dollars or so...you could get this.
https://cobikes.com/shop/index.php?ma...products_id=34

It will work, but you will have to move the chain ring on the inside of the cranks.

It's possible to use a spacer on the rear hub to move the cog out a bit; then you can use the 107 or even 109mm spindle. I wouldn't obsess over all the mathematical calculations coming out just perfect; not that critical to be perfect, just close. Bicycle chains are flexible enough these days to handle it. The angle of deflection caused by being off by 4mm over the distance beteween crank and rear hub is quite small. inverse sine of 4mm/500mm = <.5 degrees