College is the first part of the path. College expenses have soared since I was in school. But the method that worked for me is still available. Namely, we had very little money at home, to the point where no 4 year school was affordable. I had worked my junior and senior years of high school, not that it would have come near covering college costs, but it helped give me at least some spending money in college. The main thing was to select several schools and see who would come up with a good enough financial aid package for me to afford to attend. I wound up with the maximum in loans, the maximum in state and federal grants, the maximum in summer job earning requirement, maximum in work-study, and an aid plan that meant I'd graduate with zero dollars in savings. The rest, which was a lot, was scholarships from my school -- Northwestern University. That meant that I'd wound up at the most expensive school I'd applied to. The least expensive was my state school, which said that they'd give me much less than they thought I needed (and agreed with Northwestern about how much I and my family could come up with). Easy decision, even though they'd originally been my first choice.
Something that is more an option now than back then is to spend your first two years at a community college. Expenses are much lower, and the standard freshman chemistry/biology/physics/calculus are taught by people who are interested in teaching them, versus four year schools where it's often viewed as undesirable to teach such classes. I took Calculus III and Ordinary Differential Equations at my local community college and was very happy with the results.
As I was selecting colleges, I heard that the typical college student changes major 3-4 times. So in addition to the Electrical Engineering and Computer Science that I planned to major in, I also required that the school have a good Astronomy department and one or two other things. This helped narrow the field, and it ensured that if I decided I didn't like what I started with, I could change major to something else and still be in a good department. First I changed to just Electrical Engineering. Then to Applied Math. My area of application was originally supposed to be fluid dynamics, but that sequence was cancelled. So I jumped over to Astrophysics for my application area.
A couple of things I did in college worked out very well, and even better for my sons since they didn't have to take time to figure them out after they got to college. First, regardless of what area(s) you're interested in, join up and be active in the student groups for that interest. Different fields have different personalities, so you can get clues about whether you'd be happy in that field early on. The student groups also have more information on just what the field is like. Also join the more general groups, like Society of Women Engineers or National Society of Black Engineers (two excellent groups on my campus, probably our best-run).
Second, is to make some kind of connection -- maybe a job, maybe volunteering -- to work with someone in research. This is what I did for work-study the last two years of college. It gave me excellent practice at doing science as opposed to just taking classes about science. And it gave me a good working relationship with someone active in a field I was interested in (ice ages and climate change).
Thanks to my experience working with a professor while I was an undergraduate, I realized that my graduate school experience would depend strongly on whether my adviser was someone I could work happily with. You spend a lot of time with your adviser. If you're dreading each meeting, every day, it's going to be a very long and unpleasant time in school if you even get the degree. On the other hand, there are a lot of different people and types of people, even within the department. And many different departments in the country. Again, I was not as concerned about exact area of research I would do -- the universe is interesting. At one school, I'd have been doing theoretical climatology, at another I'd have been doing numerical models of tornadoes. At the school I went to, the University of Chicago, it was polar oceanography. While I was happy enough with the people I talked to at the other schools, my adviser and several other faculty were a step above in our conversations.
After graduate school, it's likely that you'll spend time in a postdoctoral position. Almost certain in biological sciences, likely in physical sciences. I earned an unrestricted ocean modeling fellowship -- meaning that I could do my ocean modeling at any school, with any adviser, that I chose. It's a great setup, though rare. More typically, you'll be reading help wanted pages of your professional society's web site. Anyhow, during this phase, be looking for your next job starting from day one. (I waited, which was not a good idea.) Most postdocs are only a year or two, so you'll need to be looking either for your next postdoc or a longer term position.
Every two or three years, there is a flurry of reports about the 'looming terrible shortage' of math/science/engineering people. Often, they include comments about how anybody who earns a degree (or, specifically, doctorate) in these areas will be flooded with offers. These articles have been common since I was an undergraduate, and I've seen sources saying so since the mid-1960s. There has never been a shortage in the sense of fewer applicants than jobs. The major report that came out when I was in school, which contributed to a surge in graduate students in math/science/engineering, turned out to have used fewer than 3 applicants for every 2 jobs as its definition of 'shortage'. My friends who were among the 1 in 3 who did not get jobs in science disagreed with that definition. Things are better now, but there is not, and never has been, a guarantee, or a shortage. So thinking about your job hunt much earlier than I did (not until after I defended my thesis) is a good idea, basically a requirement.