Ya I would say start off with black and white film first. Get some TMAX 400 or better yet get some of this
Same film as TMAX but much cheaper. Of if you want to try color negative film get some Portra 160NC or VC.
As far as developing film yourself, it's not hard and I'd strongly encourage you to try it at least once. You don't need a full darkroom setup to develop film either. All you need is a light sealed room like a closet, chemicals, and a tank and reel. I'd suggest getting some HC110 developer since you can dilute it so you only use how much you need for a roll or two. I'd say you could probably get everything you need to develop a few rolls for under $50.
Once you have your negatives you can just scan them in. I'd try seeing if your school has a digital photo lab/ computer lab where they have nice scanners. Most schools will have them if they have a darkroom. But if your school doesn't and you still want to scan your negatives in, buy a Epson 4490. It's probably the best bang for your buck scanner out there. Plus you can find them for under $100. If you really want to go all out buy a Epson V500, such a rad scanner and worth the higher price tag.
I'd just search around the internet or go to your library and check out some books on film. Just go out and shoot as much as possible and see what you like and don't like. Do some researh on photographers and pick out what you like about their photos and try to incorporate it within your own style.