XBOX inputs are USB (even though the connector may not look like it).

Yor best bet as far as cost and connections go is to build a low cost PC into your cabinet. You have a large choice of more than capable graphics cards, all with NTSC output to suit your needs as well.

Using an XBOX would be like using scuba gear to feed your goldfish.

You should have plenty of choices for joysticks as well, whether you decide to retro-fit your own from old arcade machines or old computers (WICO positively made the best joysticks to have ever hit the market in the history of joysticks) or if you decide to buy something pre-built to suit MAME and a wide selection of games.

I haven't looked at any plans for cabinets, but from the ones I've seened open, you should be able to build something fairly easily. Next you have to decide what orientation screen to use... :) There should be software to help deal with issues like this too.

Bruno