Welcome to the airbrushing world. There's a veritable treasure trove of information out there in the interwebs, so let me see if I can distill down my advice. I've been using airbrushes since I was a teenager, but not much for railroading; I've been building plastic models for even longer, although my pace these days is really...slow.
I started with a drugstore special Testor's single-action airbrush, run off propel cans (Remember when drugstores carried hobby stuff? No, I'm talking in the 1980s, I'm not that old). Simple, easy to use. Probably breathed in enough fumes to give me lung cancer someday. Advantage of propel cans is you generally don't need to worry about moisture in the air, like with a compressor system.
These days I have two brushes, an old Badger 155 Anthem and an Iwata HP-B. The former is for large area work, the latter for detail. I assume you are planning on doing detailing/weathering, so you might as well start with a double-action brush, assuming it's in your price range. I still use an old Badger 80-2 compressor, although I've added a regulator and water trap. I'm sure there's plenty of affordable options for compressors out there, as suggested by others above.
Tips and other things I've learned over the years:
-If you're spraying indoors, get/make yourself a spray booth. Doesn't have to be anything special, I actually use one of those large clear plastic storage boxes you see at Target or the Container store. Turned it on its side, cut a hole in the bottom and installed a fan from Home Depot, connected to a short segment of flexible ducting. I cut up squares of furnace filter to put over the intake and replace when they get covered with paint. My workbench is near a window, when I'm spraying, I just open the window and put the end of the ducting out the window.
-If you're spraying indoors, especially if using enamel-based paints, wear a respirator. One of the basic cartridge ones from the hardware store should be fine, and will last many years considering we aren't painting nearly as much as say a home painter.
-Make sure your compressor system has a good water trap, especially if you live in a humid area. If you live in a dry area like the desert, you might be able to get away without it, but it never hurts. Water in acrylics may make it thinner than desired; in enamels it can ruin a paint job.
-Just starting off, you will probably need to thin the paint more than you think. It took me years to realize I started off spraying paint way too thick. For models, I generally thin until the consistency of "1% milk." But depending on what you are doing, you can go much farther than that. For example on light weathering or shading, you may be shooting basically tinted thinner, going for a very light coat. Experiment, see how different mixes come out.
-I use both acrylics and enamels, depending on what I'm looking for and/or how lazy I feel at the moment. I do use hobby manufacturer's thinner for airbrushing however. I know many people claim distilled water works fine for water-based paints, but I've not had as much success doing that.
-For cleanup, however, I use lacquer thinner (can at the hardware store) for enamels, and isopropyl alcohol for water-based paints. Again, yes you can use water for cleaning out the brush after water-based paints, but I find alcohol is more thorough and dries out much faster.
-If you don't want to buy a bunch of jars for a suction-feed airbrush, look around for other things you can modify. I use old plastic film canisters with a cap modified to take a suction feed tube. Paint doesn't stick to the type of plastic they used, and with the cap on, it's almost airtight. I'm probably dating myself now, but you used to be able to go to any photo developing store and ask if they had extra leftover film canisters. Today, it's "film? What's that?"
-For fine demarcations, use good masking tape. I like Tamiya's hobby masking tape. I also occasionally use liquid masking, where you paint it on, then after it dries, use a sharp knife to cut off the masking you don't want.
-The biggest hassle? If you're like me, you'll find you spend more time prepping, masking, mixing, and cleaning up than you actually spend spraying. Is it worth it compared to a regular brush? Yes. Usually.
-And finally, as mentioned by others, practice. Try scraps, old cars, re-paints. Experiment with different brands of paint, mixes, thinners, pressure settings, how close to hold the brush, and so on. Learn when you might need a primer coat, or top coats. Discover how difficult it can be to paint gloss white or a metallic coat. Don't expect great results right away, it's a learning process. And if it doesn't come out the way you wanted, you can always re-paint it. Or blow it up with firecrackers.
Good luck to you.