Hi Graham
When new to airbrushing I did the same thing that you're planning to do.
I bought a cheap industrial compressor (one of the ones that comes with a nailgun and tyre inflator etc.) and a generic Chinese double action airbrush. The airbrush wasn't too bad - gave pretty reasonable, if slightly inconsistent results - until I lost a part to the carpet monster and found out why they were so cheap. No spares, no service, no working airbrush.
The compressor was fine as well - but so incredibly noisy that I could only use it during daylight when no-one else was in the house.
After finally tiring of this and looking at modelling forums, bought the best airbrush I could afford and a silent compressor. As I live in the UK, this was quite a commitment, as Hobby products and just about everything else cost far more than they do in the US. The difference to my modelling and my sanity has been immense. I can airbrush whenever I want, and the quality of my paintwork has improve immeasurably.
My advice would be to save up and buy a reputable double action brush - Iwata, Badger or a comparable make (I got an Iwata, but I believe Badger are very good too) and a good quality silent compressor. It may be expensive initially, but will save you money in the long run, depending how much modelling you plan to do. Also, if things go wrong, you'll have decent warranties and/or the chance of buying spares.
And remember the old saying - he who buys cheap, buys twice.