To become an project leader in an industry or government research laboratory (Ph.D.)
To teach and/or do research at a university (Ph.D.)
Masters or Ph.D.?
A Ph.D. will take 5+ years. The first 1-2 years you will take additional classes, spend time in different labs to see what they are doing. By the end of this time you probably have picked out the lab and problem you want to work on. Usually you then take qualifying exams and write up a research proposal. Once this is out of the way you will spend 2-3 years doing research and writing up your results. Finally you defend your thesis before a committee.
A Masters generally takes two years. Some consist entirely of additional classes (a non-thesis Masters), but most demand a research project as part of the requirements.
Which school?
This is largely up to you. There are several factors to consider.
Do you want to be in a particular part of the country?
How qualified are you?
Which schools offer the program you want?
Are there good people working at the school?
Who will give you a good deal?
In the end it is often a good idea to try the 'shotgun' approach. Apply to some schools that you think are beyond your reach, some that look just right and a few that you feel should certainly accept you.
How do I get accepted?
Get a Biology degree from Eastern.
Do an independent study. This is usually the most important thing you can do. To quote the graduate admissions director at Yale 'The best predictor of success in graduate school is the completion of a research project as an undergraduate'.
Make personal contacts. Work at a lab for the summer. Read their papers and write or email to them with questions. However, don't become a pest or waste their time with trivia; if you ask questions, make sure they are good ones. Find out if any of the faculty know someone at the school you want to attend.
Present your work at meeting and/or publish it. This is sure to get attention, since very few undergraduates will do this.
Do well of the GRE exam. The general exam covers Math, English and thinking ability. The Biology exam, required by many but not all graduate schools is similar to the Biology Department's Yearly Comprehensive exam. Note: do not try to cram for these exams. Your best bet is to prepare for them over time. Take practice exams, read general Biology texts, practice basic math skills, all on an on-going basis. As a quick rule of thumb, if you are not scoring close to 100 on the Biology Yearly Comprehensive exam, you need to put in more time.
Maintain a good GPA. You don't need a 4.0, but a 3.0 is probably a good idea. If you have less than a 3.0, you can make up for it by doing well in the other areas listed above.
How do I pay for it?
Usually you don't have to! Almost all Ph.D. programs will only accept you if they have money to support you. In general you cannot expect to do the kind of work that a Ph.D. demands and have an outside job. While graduate stipends are not great, you can live on them, though you may have to share an apartment or house with others.
Masters degrees are often harder to finance but, since they only last a couple of years, you may be able to take out a loan. In some cases you will be able to get a Teaching Assistantship, which will require teaching a lab or two each week.