I just bought a Black and Decker corded one that works off either AC or DC and it works just fine. Even comes with a needle for balls and a couple of attachments for blowing up kiddie toys like rafts and swimming pools.
I guess the advantage of an actual air compressor rather than an "inflator" is that they have tanks of compressed air and can power the air tools, whereas the little inflators can't. I've never needed an air compressor for anything except inflating toys and tires though so it's a wash for me.
$15 tire patch kit from your auto-parts store, and this Black & Decker ASI300 Air Station Inflator
Looks okay. You just never know. I've had this black and decker one for 12 years and it's saved me on the road inflating low spare tires many times.
BLACK+DECKER ASI300 Air Station Inflator https://www.amazon.com/dp/B000IE0YIQ/
At least for the E90 3-series, you can buy a spare tire kit from I think the X3 or some such, which will fit the car nicely. It does take some space in the trunk, though: http://www.e90post.com/forums/showthread.php?t=382545
I switched from run-flats to conventional tires ~2 years ago, and bought the spare tire kit and threw it in the trunk. I also have one of these tire inflators in the trunk for emergencies.
Looks like Bav Auto sells kits for each specific model of E90 3 series: https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=e90+spare+tire+kit&tbm=shop