As Biomath is not a department, but an "interdisciplinary program", you should go to the math adviser (3rd floor, Hill Center) for course-related questions. They should be able to handle issues of requirements and such.
Generally speaking, the major is probably best suited for grad school in applied math, computational biology, biomedical engineering, or pre-med (see suggestions regarding pre-med courses on the website). It is less clear what jobs are available with a Bachelor's degree in biomath. If you are not heading to a graduate or professional school, perhaps it is best to double major in another discipline.
You should look at the general hiring for biology majors (genetics, etc) and apply to those jobs. Many, or at least some, of these recruiters should be very interested in someone who has the additional math background.
For one thing, it is a great idea to attend the BioMaPS seminar.
There is no formal link between biomath and BioMaPS, but students with a biomath degree have the perfect background for applying to BioMaPS.
Regarding research at Rutgers, during the year as well as summers, the best is to, once again, look up opportunities available to life sciences majors. Contacting professors associated to the BioMaPS program whose research you find of interest is also a good idea. Eventually, however, an REU experience (probably out of state) would be optimal.