Most common from what I've seen are
-threaded as John mentioned, denoted with simple OD size and thread pitch
-"long taper" which are denoted L00, L0, L1, etc
-"camlock" which are usually denoted D1-3, D1-4, D1-6, etc.
This isn't all-consuming, but encompasses probably 90% of what's out there.
As far as workholding, I'd concentrate first on a 4-jaw chuck as that's most versatile. Collets are a nice secondary addition. The 5C collets are the most widely produced and thus the most economical to buy. There are untold numbers of other lathe collets out there, I'd say 2J collets are probably the next most common, after that they go pretty quickly into rare birds, harder to find and thus usually more expensive.
As far as workholding with a collet, you need something to "clamp" or "close" the collet. This can be something like a Hardinge/Sjogren "speed chuck" which attaches to the spindle, it can be a hollow tube with threads on the end which closes the collet into the spindle nose (or usually an adapter) via screw pressure, or a lever closer which starts with the same hollow tube, but uses an over-center locking device to actually close the collet.
These two sites have some decent pics which will help with visualization and some numbers too.
http://www.shopswarf.com/chuckmt.html
http://www.shopswarf.com/collet.html