Get yourself some cheap 4-pin MASTER locks to start with .... After you get the hand of these, get a lock that has a removable cylinder.
Take it apart and look at the innards .... (Note: You'll need some sort of plug follower and tweezers). You will learn a lot more about how a lock works and how to pick it by doing this then you will picking a lock that you can see pins setting, etc. (Cut-aways, etc).
These don't have to be new locks. In fact, for the first couple "guttings", its probably better that they aren't as most people will forget the plug follower and spray springs and pins all over the place, never to be seen again.
That's the voice of experience BTW ....
Taking the lock apart and looking at all the pieces will help you get a "mental image" of what is going on inside the lock as you pick and hear the various sounds such as the "click" of a spool pin setting or the "crunch" of a serrated pin.
If you want to see a "transparent / cut-away" lock being picked, there are all sorts of videos on YouTube that you can watch for free.
or this one, 
I'm open to suggestions on other locks to look at.
