California alone among American Bars does not require a law school education for Bar admission.
Internet law schools are crap. Sorry to be blunt. But I spent 9, arguably 10, years in law schools so I should have some right to an opinion. (And no, I never flunked anything; I studied in different countries.)
As you rightly noted, law schools don't look for any particular major at all--in fact, almost any academic subject is a fine choice when it comes to picking a major that will look good on a law school application. Although there are certainly "traditional" majors that students interested in eventually pursuing law undertake (economics, political science, etc.), there is no one "perfect" major when it comes to preparing you for law school. There are some majors (particularly those that aren't strongly academic, such as the arts) that may place you at a slight disadvantage but, even so, plenty of students in those fields get admitted to law school every year. If you major in something you love, then you have a greater chance of doing extremely well in school, which will translate to a high GPA, which will in turn increase your chances of admission.
The key is not so much what you major in but, rather, what you do within your major. Aim to do the following:
1. Pick a college major that will require a lot of reading- and research-intensive classes. Political Science falls into this category nicely, as does Business, English, Economics, Psychology, Sociology, Philosophy, and many others. Picking a major of this sort will not only prepare you for law classes (which themselves are incredibly research- and reading-heavy), but it will also demonstrate to law schools, when you apply, that you can handle the academic load of law school.
2. Keep an upward grade trend throughout college. This means that your grades either get stronger as you go through school, or start off strong and remain there for all 4 years of college. Most law schools will want to see GPAs of 3.5 or above (the closer you can get to a 4.0, the better).
3. Take a challenging class load: Intro classes are okay for freshman and (maybe) sophomore year of college, but once you get to junior and senior year, your focus should be on upper-level classes and seminars that allow you to really hone in and focus on your specific interests within the major. And, as always, keep your grades up throughout.
4. Establish rapport with your professors (particularly during your junior and senior years of college). You can do this by attending office hours, working for them as a research assistant, and talking to them after class. They will be the ones writing your letters of recommendation, and will only be able to write effective, overwhelmingly positive ones is if they have specific, anecdotal knowledge of you and can favorably compare you to other students in your class.
Another useful thing you can do, regardless of your major choice, is to take formal logic courses (which can be found under the Philosophy Department at the college you end up attending) during your sophomore and junior years; this will help you later as you prepare for the LSAT.
It doesn't hurt to start thinking about what else you can do in college to maximize your law school chances:
1. Work on your extracurriculars. Don't worry about being a part of 30 student groups; instead, focus on 2 or 3. Become a part and get involved during your freshman and sophomore years, and then obtain leadership positions in them during your junior and senior years.
2. Take the LSAT either the summer after junior year or the fall of your senior year of college. This will allow you to get the LSAT out of the way and apply as early in the admissions cycle as possible, which is incredibly beneficial to your overall chances.
3. Research law schools and become familiar with their LSAT and GPA requirements, as well as their acceptance percentages. Law school admissions center around your GPA and LSAT combination, so knowing where to aim is definitely a plus. A great place to start is the LSAC Official Guide to ABA-Approved Law Schools: http://officialguide.lsac.org
I know I gave you a lot of info--I hope some of it was helpful! Good luck with everything, and please let me know if I can be of further assistance.