About visas..
Almost all visa listed on the Japanese visa site linked above (and here:
http://www.mofa.go.jp/j_info/visit/visa/appendix1.html) spell out pretty clearly that you need a Degree or 3 years of experience in the field to acquire a Work Visa.
I met some teachers teaching without a degree - they were all either on spouse visas or working holiday visa. I met teachers without a degree who wanted to stay in Japan but, after their working holiday visa ran out, were forced to return as there was no other option for them to stay.
The following is just sort of what I've picked up from talking with bosses and co-workers, so y'know, take it with a grain of salt: Japanese immigration is sorta notorious I guess for bending/creating new rules and covering all of their activities in mystery/secrecy. I wouldn't say it's -impossible- to get a Visa outside of those guidelines on that website, but I would say it's next to impossible.
To the OP, I would say these are your options:
Working Holiday Visa (1 year only)
Tourist visa (3 months, renewable a few times - but you cannot work)
Work Visa (Requires 3 years of experience or a college degree)
Language School
Exchange Student
I don't know what your financial situation or university options are like, but if I were you, I'd consider finding a university with a strong international exchange program. This would set you on a nice path to get some exposure of Japan while still keeping up with school. Then, once finished with school, you'd have some nice inroads into getting a job in the country if that's what you want.
OR
Do the 1 year Working Holiday Visa in between HS and Uni. This'll give you a lot of good exposure to Japan as well and allow you to save up some money for Uni. To do this, you'll obviously need to save a little money for plane ticket and first month's living expenses. Also, you'll have to find a job - which isn't so difficult. There are many, many sites on the internet full of job listings for English teaching positions and they regularly hire degree-less people on the Working Holiday Visa. Your age might be a problem for some, though - I've never seen a teacher that young in Japan. But I don't really know about that.