I started with really basic airbrushes, can't even remember what they were now, but they were cheap, poor quality and with bad to worse performance. That was so disappointing and discouraging, that I often thought airbrushing is just not going to work for me
Then I invested in a moderately priced airbrush, a Binks Wren. Very well made and it performed well for me, I still have it after nearly 50 years later. That made airbrushing so enjoyable for me, and I soon realized that you get what you pay for, cheap is usually not going to come with satisfactory results.
Now, after owning Paasche, Badger, Binks, Iwata and others, I can appreciate that it's (I think) better to start with an airbrush of good performance, even if you have to save for a bit longer in order to get it. Bad performance just leaves one frustrated with the results, and you don't advance your skills as you learn with something that is substandard.
There are Badger's, (my favorite,) that can be had when the major distributors have sales. I have bought double action internal mix Badger's for as little as $60-70 on sale, they are extremely durable and perform with very good results.
And you can find decent compressors for about $50, I understand that is a fair chunk of change, but a combined price of a bit over $100 is a sound investment, when you consider the results will surely be more likely satisfactory, as opposed to disappointment.
Have a good look at "Don's Airbrush" website, just Google that and you'll find some extremely valuable information about all things related to airbrushing. Well with the time investment.
Good luck in your future.
Patrick