It is expensive to get started, but particularly with airbrushes you really will save money in the long run. You may have to replace a needle and nozzle once a year (unless you play hello airbrush, hello floor) but the brush will last a life time. A cheaper brush you will still replace parts, plus o rings springs etc, then when it still doesn't perform well, end up replacing it anyway. Airbrushes really are one of those you get what you pay for things, they may look similar on the outside, but the machine quality, and grade of materials used to make them make them very different animals. Its a case of buy well, buy once. The major manufacturers are also pretty good at trouble shooting guns with issues, and will even refurb or occasionally replace them. Plus branded brushes are just easier to use and learn on, a lower end branded brush will be infinitely better than a cheapie, and way less frustrating to use.
Compressors can be super expensive, but unless noise is an issue, any compressor from a hardware store will do the job. They are LOUD though. Some people get these then swap out the motors for fridge motors. There are a couple of threads about it you may find if you do a search - you do need to be a bit handy though.
After the initial outlay though it's not expensive. You only need a few colours, you can mix your own, and a surface to paint on, all the rest are optional extra and nice to have, but not needed.