I would recommend not going cheap. You don't have to buy the high end stuff but no need to mess with problem products upfront.
In regards to paints just start out with Createx. Readily available and designed for airbrushes and common at Hobby Lobby and other similar craft stores. No need to thin, no need to strain, no need to do a lot of stuff as it just works.
For an airbrush I would go with something like the Iwata Neo CN dual gravity feed brush. Just a decent starter brush from a company that makes solid products.
Compressor with water trap. If you don't have one and are just starting out I would recommend either getting a pancake compressor nail gun kit as something every homeowner should likely have. They are typically loud but get the job done. I started and still use a Craftsman set up at times but mainly switched over to a small California Air Quiet flow 4710 model and very quiet in regards to compressors, light weight, and a joy to use. I also have a Fusion 1000 airbrush compressor that is very portable, small, and quiet but only bought it because on clearance for 25 bucks but also are normally in the same price range as the compressors above (less CFM however).