I'm not exactly sure what you are asking for, but I'll give it my best shot.
I guess one place to start is how much of a load the chain will handle before it breaks. You can find this out on McMastercarr or elsewhere on the net. You also have to see how much torque that your gearbox is going to output to the wheels to see if it is within the load that the chain can transmit, or if it is beyond the breaking point.
ANSI #25 steel chain from McMastercarr has a working load range around only 140 lbs.
ANSI #35 steel chain from the same place has a working load around 480 lbs.
That's just some help in designing after you design your gearbox. Simply, If your gearbox is outputing more than 200 ftlbs, then you know you should go with the #35 chain instead of the #25 chain unless you like making your pit crew work after every match.
Also, I'm not sure if this will answer it either, but oh well.
The distance between the teeth of a chain sprocket is the pitch, ie, a #25 chain pitch is 1/4" and a #35 chain pitch is 3/8". When you go with two sprockets that have the same teeth count, you can make your life easier by making sure that the distance C-C is divisible by either one that you go with so you don't need to mess around with tensioning so much.
For different sprockets though, this is a bit trickier. I'm not sure, but I think this only works with even toothed sprockets. (Correct me if I am wrong). You need to think of it as 2 triangles, and a rectangle in between. When you have the pitch diameter or outerdiameter of both gears, since they should have the same difference. You then find the difference in height, when you have the centers of both gears on the same Y axis on a coordinate plane (Note:The difference on the top and bottom of the gears should be the same). Then you just need to make sure the hypotenuse of the two triangles is divisible by whatever pitch you use and you should be fine. Just a bit of geometry, no trig needed there.
I hope that helps.. Though that sounds sorta confusing.