Ciao eahlund,
I am not yet a pilot
but I think I can give you some advices since I live in that area. If you have a car everything will be easier of course (meaning to commute from any neighborhood around or in rome), but I would still suggest you to live in the east, south east external boundaries of the GRA (which his the highway rink around rome) in order not to waste time stuck in some traffic jam (and they happen all the time). If you are not planning to get a car then, you can think of any neighborhood which is near the railway station which gets to ciampino (though if you love nature and quiet places I'd suggest you to go a bit further outside rome like frascati, colonna, valmontone, which are all small towns but with a lot of fresh air and peace
and cheaper than rome for rent and food.
Let me know if you need some more details
fabio