If you are interested in a research-oriented career, you pretty much have to have a graduate degree. With an MSc degree you might manage a lab or work in an applied field; to direct your own novel research, typically a PhD is required. Most graduate programs allow you to switch from one to the other once you are admitted. Most of the research-focused, high-reputation graduate programs admit mostly or exclusively PhD students. You do not need an MSc degree before applying for a PhD program.
Know that in grad school, unlike college, you usually get a salary and your tuition is covered. You should ask details about how this works when you are interviewing for a program, but you should also seek advice and suggestions on this from your advisor and from every grad student, postdoc, and senior undergrad you can find (especially your lab mates). Do not be shy about this! Your lab is your (second) family, and everyone will be happy to help you or at least recount their own experiences.
Also, look around for other resources. This is your life: research the right information just as you would for a project. There are many websites that give advice on how to get into and do well in grad school: e.g. Matt Might, what grad school is like, a blog by Duncan Watts (arguably a very successful scientist) on serendipity in getting into science.
Once you know you want to do it, figure out where to apply and when. You must start this process early (see the advice on applying); plan to write inquiry emails to prospective advisors in the summer a year before the fall in which you want to start grad school. It will also take you a while to select the programs to apply for - again, seek advice on this from more senior undergraduate students as well as your research advisor and everyone else you know.
Note that in science, and especially for PhDs, I think the most important part is selecting your prospective advisor - no other parameter about the program, the university, the city or the region has more influence on your future career.
Also, apply for the NSF GRFP. These are grants from NSF to pay you in grad school, something you don't need to live (see above), but they will make your life a lot easier (because you will have to teach less), AND they will make getting accepted into a good program easier. Assume you will write one in your senior year, and another one (or more) once you've already started grad school. Talk to your prospective advisor (!!) in detail about this as soon as you are admitted anywhere.
If you are a student applying to my lab for graduate school, note that there are several possible programs you could apply to. Choose at least two; your work in my lab will be largely independent of which program you are in, but your peers, financing, and required courses will not be identical. As I said above however, all these are only marginally important in my opinion.
You can also choose a minor in any of the above programs or in the following:
If I don't respond to your initial inquiry email, wait two weeks and email me again. Make sure your email address is set up to show your full name as sender (not a nickname or partial name). Do not take non-response personally, I get a lot of emails. However, do try to get me to respond and don't give up after one try.
A few more thoughts on applying that are not included in the general application advice page linked above:
- I told you what I think matters here. Things that matter so little that we are vaguely put off by even seeing them on your CV: which languages you speak; which languages you can program in; which MS Office software you've used; your hobbies.
- no writing is ever good before getting feedback from someone else. That also goes for your CV and personal statement: show it at least to your research advisor, or another professor! Also show it to senior students or graduate students or postdocs - that's one of the benefits of doing a research experience in a lab that has such people.
- definitely list any manuscripts you will be an author on, even if they are 'in prep'. Make sure you ask your research mentor about whether there are any, and what the title and author list will be. Make sure you mention them both on the CV and in the statement, and make sure you can intelligently comment on the insights of the entire paper even if you only contributed a tiny part to it. This is also true if you are not a coauthor but helped in some way.
- Your recommendation letters ideally come from research-active professors who knows you well. Getting such people is one of your goals in college. 'Knows you well' means has worked with you, ideally over multiple semesters. Class teachers are not good. It is better to get only the required number of letters but have stellar ones than get an additional mediocre letter (not all your reviewers will read all the letters). If you are at all in doubt about your letter-writer's experience in writing recommendation letters, or if you are getting a letter from someone who is not a scientist at a university in the USA with a graduate program, refer them to this page.
- inform yourself a bit about how the actual process works. For this, you need to ask someone who knows this answer. Mostly, this is a professor - most likely your research advisor. People who have gone through the process (e.g. graduate students) don't necessarily know why they were admitted, or what the process actually was. This article explains some of it, but note that there are significant differences between disciplines.