In some ways this is like describing the color blue to a blind man; it can be done but you'll never know how much it helps, until you try.
To try to sum up:
1 you want an airbrush and a compressor
2 Money is an issue (your not alone there)
3 noise is less of a problem as you building in a basement
4 you're asking for advice on a combinations of airbrush and compressor.
................My thoughts ( they are worth exactly what you've paid for them)
1 &2
buy the best quality equipment you can afford for now; knowing that, with experience and time you will, likely "move up". Thus at a later date, because your new knowledge level and exuberance will be your guides.
Cheapest compressors = no reservoir tank, no pressure gauge, no moisture trap, no adapter for the hose connection etc. etc.
As price goes up more of those items will be included or readily available as add-ons for a discount.
Result: look for deals/sales/ combinations on the internet and/or at brick and mortar stores for a compressor having as much as you can get toward your current "ideal set up"
3
noise is an issue as time goes on. So the quieter the compressor ( or use of a sound dreading cabinet or ??) will pay dividends in your future, as you age ( truefully we have-despite our denials) . Besides, how you gonna hear your tunes if the compressor is too loud?
4
So gather facts from the web sites of manufacturers of compressors and air brushes ; make up a file so you can compare apples to apples and then look for the deals at your price range. then with those facts you can ask things of the forum about specific items
Never the less, you are starting what is going to be a grand experience of learning and doing and getting to share with others what you have done; all the while getting better and better.
We are all rooting for you and want you to succeed.
"Tools do not make a craftsman, but a craftsman makes the best of his tools, to create his art"