I'm not super up to date on the ArcadeVGA but I assume you would still need one.
As for the computer, if you're playing 90's and older games would you also be playing 3D games from the 90's? Gauntlet Legend, etc. If not, depending on the version of Mame you use, a 1Ghz proc would suit you fine.
Personally, this is what I go with for any MAME build I do now. It's powerful enough to run all the 2D games as well as MAME can handle and 90% of all the 3D games:

You can take the case out if you like mounting the computer inside but that's generally where I am. I also like building the computer versus buying a pre-made. And if I'm building a full size cab, I always do this versus ITX just because it's cheaper than a 200+ dollar ITX system that's not as powerful.