Skip the cheap badger airbrush with propellant can. Thats not any better than spray paint cans. You won't really learn any good airbrushing skills with that setup. You will just get frustrated. Harbor freight has a small compressor, Item #97080. It runs $55.
It is meant for small air tools but works well for airbrushes too. It is louder than an airbrush compressor but only runs when it needs to fill the tank up. You will also want to add a water trap so that you do not have water coming through your airbrush.
An airbrush compressor used will be in the same price range. A new quality one will run 80-100. They run quiet but pretty much run all the time.
Start with a Paasche H or equivalent name brand airbrush. A paasche H can be had for under $50. This is a great starter brush and a work horse. I still have and use my H after 20+ years of modeling.
You will learn more faster and have more fun with this type of setup. Also check online for DIY airbrush booths. It wont be long before you start stinking up the place and annoying the family from all your over spray. You can usually build a spray booth with stuff you already have around the house.
The dollar store is a great start to getting sanding sticks, tweezers, files, tape, clips and clamps, snippers, scissors, toothpicks, cotton swabs, etc. Go down every aisle, even the cosmetics. You will be surprised what you can use for modeling once you see it through a modelers eye.
As you skills increase your tools will get finer and demand more presicion and you can spend more then.
Ebay is a great place to get used kits cheap. Join a model club in your area. Modelers are always willing to help and may even donate a kit and some tools to you as a new modeler.
Get to know your local hobby shop and go to modeling shows. The vendor area is a great place to source cheap kits and hobby tools.
Buy nicer fine paint brushes. They last longer and offer better control and are not much more money.
And most important is to remember that there are no failures in modeling. If something goes wrong, there is always to a way to correct it. I have been modeling for 35 years and still make mistakes but have never shelved a kit beacuse I could not correct the issue.