Dude
Congrats, I loved my time at Ramstein. Do a search and you will find lots of info. But in a nutshell, there is stairwell housing (apartments) on base but they are cozy. The pros are a short commute to AAFES and work, and no need for a second car; and the downside is you can have a tendency to get stuck on base for weeks on end and not truely getting the full German experience, which is a tragedy. There are lot of places to live off-base, whic is notce to be in a little German village and drink Pils with the locals; but it can get expensive (living off base, not the beer...it is worth every pfennig or euro-cent, whatever they are called nowadays!).
As for cars, an American car really isn't a problem as Americans have been bringing them to Germany for over half a century; but parts can get expensive and some things like emmissions control items are not found in Europe and can be a problem if they break. I had that problem in Belgium, my check engine light came on and the local VW dealer could not fix it as they didn't know what the code meant. I would recommend against a big American car/truck/SUV simply because gas is still expensive even on base and driving one through those small German villages can get touchy. Plus you stand out like a sour thumb. Buying a late-model German specs used BMW or Audi might make more sense, but there isn't really a huge advantage of one over the other. I shipped a VW Passat over and bought a used German-specs BMW 3-series, it worked out great. Oh, and there are tons of "tax-free" sales if you are looking for a deal. Check out the European version of the Stars & Stripes on-line here and look for the ads.
Cheers! M2