Propellant cans are evil. They do get cold, and their pressure will drop, and the pressure isn't very reproducible all of which can lead to problems with airbrushing, particularly with one new to airbrushing. Although I do think that even an el cheapo airbrush is better than a rattle can, both in quality of finish and paint selection, I definitely think that stepping up to a Paasche H with a compressor would be the way to go. I started out with a really cheap Testors airbrush w/propellant can and bounced around through a variety of air brushes. Had I known then what I know now, I would have gone with the Paasche H and called it good. If you don't mind buying online, take a look at dixieart.com they have good prices and free shipping on orders over $45.
As for painting your Zero, you'll need to do some research on the color separation lines. Some camo was painted free-hand with fuzzy lines, some was masked to give tight boundaries. Going by your description of the box art, it sounds as though you'll want to mask. For spray color order, generally you want to spray dark over light, and if I were building a green/gray Zero, I would do the underside first, then the top.