Type and strength of a typical chain
There are several different sizes of chain based on the number of sprockets used in the rear cluster (e.g. 8-speed, 11-speed).  These are 3/32" nominal width.  Single sprockets for these chains are available, but can be hard to find and/or expensive.  In your application you may be able to get away with a slight mismatch, i.e. using a wider chain than your sprockets would suggest (an 8-speed chain on 10-speed sprockets, for example).  This wouldn't be a good idea on an actual bike, and it could get fiddly if you mix and match too much.  Here are the relevant spacings.

The alternative is singlespeed components - they use 1/8" chain and sprockets are always sold singly.

If you're going to pick up cheap used cassettes, I suggest you pick one type and stick to it.  All 8-speeds should work well together, or all 7-speeds, but less so for higher counts.  7- and 8-speed parts are cheap if you want to buy some new, while 5- and 6-speed can be hard to find and 10-speed or higher will get expensive.

As for the strength, consider the forces involved in hard pedalling - let's say a 100kg rider standing on a 175mm crank with the chain on a 22-tooth chainring.