hey welcome back!
As long as your compressor has a 1/4" adapter to it... OR has an adapter you can screw another adapter to get it to 1/4" you are set!
I recommend at the least a regulator too if yours doesnt have one already.. about $20 to $60 dollars depending if you get an industrial type one from Lowes and such, or a hobby type which can be had from
dixieart.com or your local hobby shop perhaps.
A moisture trap is nice as well, especially if you live somewhere with a bit of humidity. It is $19 at Lowes or your local hardware store. (They are all basically the same, construction or hobby moisture traps/filters do the same thing)
AND if you get these wonderful things, remember you will need one 1/4 connector for the end of each of them. (one from the regulator to either a water trap or the airbrush, and if you get a water trap one for the end of that for the airbrush hose) Those are cheap at about $1.39 each and can be got at a hardware store as well....
Mike answered the question about nozzles... once you decide which brush to get play with a little before you paint a model... even spraying water with food color in it will give you a rough idea how much or how little it will do for you.. (and its cheaper than model paint!)
I have a Badger 175 and it is a good brush, HOWEVER... I recommend the 155 if you are doing hobby stuff. It goes in tighter for fine detail and does good at general coverage for bigger models. The 175 had a bit more of paint output and IMHO it is taking me longer to learn how to control it for the detail work than the 155. The Badger 360 is the same brush as the 155 with a gravity feed option which allows you to get even lower pressure and therefore possibly finer detail work in... Either one are good and easy to clean. (Do a search for cleaning airbrush on here and you will see as many posts about it as which one is the best one!)
Good luck! And hope this doesnt confuse you even more!