I guess I'll be one of the few people that will eagerly tell you to go for it. It's really fun, it's cheaper than driving a car, and it's more flexible than you might think -- I've met people who ride a motorcycle almost all the time, all year round, only taking a car for a grocery trip or something. A highschooler who just wants a cheaper way to get around should have no problems at all, especially while keeping a backup cage.
That said, your two biggest obstacles will be the detriments numbered 3 and 4 (1 and 2 can be lessened by being smart while riding). Riding in the rain isn't crazy hard (just take it easy), but dress up in a warm, waterproof outfit, and pay extra attention to cleaning/lubing the chain. Riding through winter can also be done (and has been done by others), but only if your area is efficient at street plowing, and only if you can stand the cold and have something warm enough to wear.
As for the lack of storage space --
make some! Wear a backpack, get some saddlebags, and/or buy a jacket that has deep and numerous pockets. I've ridden with my school backpack many times (and that's probably stuffed with more stuff than you'd need from a store anyway), and my jacket has a pocket that's perfect for a few DVD cases, a small- to medium-sized bottle, or other small items.
Moving on to the actual riding, the first thing I would recommend is to take a Motorcycle Safety Foundation (MSF) course (of which
these people seem to be an associate). It's very much worth the money, because it'll teach you all of the essentials in riding, likely lower your insurance rates, and make the whole licensing process easier (completion of the Basic RiderCourse
waives the DMV road test, although you still have to do the written test for the permit). It's nothing like ordinary driving schools, because instead of learning "red means stop. Green means go," you're learning how to corner properly, dodge obstacles, make emergency stops, etc. It's similar to the license tests in Gran Turismo and Tourist Trophy, actually.
As for the bike, it's hard to go wrong with one of the big-name Japanese manufacturers in terms of build quality, and if you know what you're looking for in the type of bike and engine displacement, there isn't much I can tell you other than "keep looking." I will tell you, however, that you'd be a bit hard-pressed to find a ZXR400 or RVF400 in the 'states, considering they weren't officially imported here. I know there are plenty of Ninja 250s and 500s around, but I don't know Hondas well enough to know what <600cc sportbikes they sold here during the '90s.
If you have more questions I'd love to help.