First, I recommend taking it one step at a time. Mame has a lot to offer, but there are a lot of features and variations that involve a lot of exploration to discover and appreciate. Mame is really fun to play on your PC in it it's simplest form: Mame32 using a gamepad, without a cabinet. Or better yet, using your PS2 Arcade Stick & converter. If you are thinking about building a cabinet with a 15 inch PC monitor and a PS2 arcade stick, I don't imagine it would play much differently than it would on your desktop.
I used to rearrange my desktop to put my monitor near eye-level, and put my big beefy controller on the desktop so I could stand up and play, to get the arcade feel. That was an Ok temporary solution until I started getting the arcade cabinet to work.
If you're going through all the trouble to make an arcade cabinet, it's really worth taking a look at some of the great options that are available FIRST so that you don't build the cabinet once, and then decide that you've got to throw it all away to make the one you REALLY always wanted.
Here are some good starting places:
Start at the main page here and peruse all the stuff on the left pane - controls, monitors, software, examples, (etc.):
http://www.arcadecontrols.comErr, uhhh, yeah - what DaveMMR said: check out that message thread he mentioned.