Just start with MESS. The best part is, if you already know how to work with MAME then you know how to work with MESS, because they're essentially the same thing. Lazy man's dream!
I don't know how MESS stacks up against the leading dedicated console emulators in terms of emulation accuracy, but then again, I don't really give a ---steaming pile of meadow muffin---. For the amount that I use it, it works just fine.