Sounds like you have some good, concrete ideas about how to proceed. Contacting professors whose work interests you, to ask about graduate study in their departments and/or labs, is certainly a necessary step.

Throughout academia, we have a rule of thumb: do not ever, ever, spend any of your own money or go into debt for a PhD. That means that any place at which you should give the slightest consideration to doing graduate work should offer you a full waiver of tuition, plus a modest income ("stipend") and health insurance, for the duration of a reasonable period of study. The rationale for this rule of thumb is twofold: First, the expected financial returns to a PhD simply aren't such that you can afford to risk having tens of thousands of dollars (or more) of debt to repay. Second, a university's willingness to spend their money to fully fund you serves as a useful indicator that they think you have real potential for success.

When you correspond with scientists with whom you might want to study, they should be able to tell you roughly how funding works in their departments. It's not the same at every university or for every student. Possible sources for funding are basically: (1) You working as a researcher in someone's lab, supported by the university and/or by grants won by the lab's PI; (2) you working as a teacher or teaching assistant; (3) fellowship support provided by the university (i.e. they just give you money); (4) outside grants or fellowships you win yourself. The normal case for scientists is that your funding mostly comes from (1), but among scientists of my acquaintance there has been a healthy mixture of all four, and nearly all graduate students in science will at some point get funding from more than one of those sources. However, what they should be able to tell you before you even apply is how many years of funding are guaranteed by the university, whether funding is usually available beyond the guaranteed years, and what the typical funding package consists of (as I said earlier, it should at a minimum contain a full tuition waiver, health insurance, and a modest stipend for living expenses suitable to the area you'd be living in).

That's pretty much all I can tell you about the funding of graduate study in the sciences, since my entire academic life has been spent on the arts and humanities side, which handles graduate funding somewhat differently. The people you should be leaning on for advice are professors at your own undergraduate institution—particularly younger ones, since they will have gone through this more recently—and other knowledgeable scientists. They should be able to separate your academic and scientific potential from your lack of practical know-how and help guide you through the process of application, from identifying places to apply all the way to deciding which of your admission/funding offers to accept, if you get that far. They will have a lot more to tell you than I possibly can about what questions you should be asking of potential grad schools at all stages of the process.

A few other notes:

• If you're noticing conflicting information about how graduate funding works, it's probably just because different departments handle it differently. When in doubt, refer to the rule of thumb above. It's ok for departments to achieve full funding of graduate students in different ways, but not ok for them to fund some students but not others, or to admit you without making it clear how funding will work.
• You could also be getting conflicting information from people with experience in different branches of science. Psychology, molecular bio, evolutionary bio, experimental physics—to pick a few—all have their own characteristic ways of approaching graduate study, collaboration, funding, etc. So it's best to get advice from people as near as possible to your own interests.
• Some science departments admit graduate students to the overall program and then let them later choose which lab to affiliate with. Others admit you with the up-front understanding that you will be working in a particular lab. Find out how it works at the places you apply to.
• When weighing offers of graduate admission, try to get some data on outcomes for students in the program, such as job placement, time to degree, and success at winning grants (especially if grants are relied upon for graduate funding). Also, talk to current students in the program, who can tell you whether the program does well by its students, or alternatively makes life tough for them, e.g. by screwing them out of funding.
• A really serious round of graduate applications does cost some money. In your comments you often seem concerned about that. Unfortunately with a total lack of support from your parents you'll probably need to have a few hundred bucks in reserve for costs associated with applying, and another few hundred bucks for moving to the area where your new school is located. If you aren't prepared to live off-campus in an apartment, which carries logistical headaches that you seem quite daunted by, all large research universities have on-campus graduate dorms, so you really would not need to do anything except drive there with your personal belongings packed into a car. Anyway, save up a little money.

A lot of these concerns are a ways down the road for you, though. You'll probably find that getting funding is easier than you might think at graduate programs you really want to get into. The best thing you can do as an undergrad is make yourself an un-ignorable candidate for graduate admission. Study like crazy, get high test scores (super important, don't let anyone tell you otherwise—this is true even in the humanities), find some ways to take initiative, and if possible form some good relationships with faculty at your college.

Good luck! Do try to get a mentor at your college, it's a much more reliable source of personalized information than pseudonymous musicologists you met on the internet. There are also books and online forums for people who want to do graduate study in the sciences, although I can't personally recommend any by name.