after I get my bachelors, check it out, and if I Ike it, stay, apply for a work visa, get the visa, contact potential employers, and hopefully land a job?
No. You get hired first, and then you apply for a work visa (with paperwork from your employer). Not all employers will sponsor visas, though, so you have to be aware of that when you apply for the job.
Also, just how long did you figure to "check it out"? Americans get only 90 days as tourists.
And also let's say that I work there for several years, and for some reason I do not want to go back to the U.S. (This is hypothetical). Is my only option to get permanent residence marriage? Is English teaching a career?
If you do not marry a Japanese citizen, typical guidelines for Permanent Residence state that you will have to be here 10 consecutive years.
Immigration Services Agency of Japan
No, your options are not to get PR, either. You can live out your life in Japan with work visa renewals (including one for investor/business manager if you decide to own your own business). Stupid, though, after 10 years. Just get PR by then.
You can also live out your life on a spouse visa. (Also stupid, and you can apply for PR sooner.)
Is TEFL a career? Yes. Is it a viable one? That depends on you and the market. If you can keep ahead of the game, you'll have it for a career. Keep in mind, though, that you will probably need to get some good credentials and/or start your own business (a headache unto itself).
Final question, and I'm super sorry if I'm becoming annoying..
How can I prepare right now to do this? I assume me studying Japanese would help because if I speak Japanese, I'm more likely to get a teaching job.
Decide on a career, of course, but I think you also simply need to come here as a tourist and look around. People have aspirations and dreams based on books, movies, and the Internet, but they may be disappointed or disillusioned upon seeing life here up close.
You can come and improve your language ability by getting a student visa to study Japanese. It will even let you work PT, but a fresh HS graduate is unlikely to land much if anything, IMO.
Re: career goals
Teaching English is one of the few opportunities here that does not require (much) Japanese language. Savvy employers will look for at least a little of it, though, as it will reduce their headaches in babysitting a teacher in daily affairs. Japanese is almost always needed in any other non-teaching job. There are exceptions, but you still need to qualify for them, and right now you don't.
Lurk on teaching job sites (like ESL Cafe). See what people are saying, read FAQs, and read as many past threads as you can. I didn't even apply for my first job here until I had done that for 6 months! Then, ask questions on those sites. You are just too naive right now to ask detailed questions, and you have not even seen Japan firsthand. No offense, but it may not be what you imagine it to be.
Japan is overfilling with teachers and wannabes. Keep that in mind above all else. In the last 3-5 years, salaries have dropped, too.