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The kids on CC get a bit obsessed with undergrad "prestige". Relax. Its nowhere near as important as they think. You can get in anywhere, from anywhere.
You don't say what your major is, but given a decent GPA (>3.4) and GRE scores (both of which are really more important for university wide fellowships than admission) you will distinguish yourself, not by the name of your institution but by what *you* have accomplished.
You want to make the most of every research opportunity, develop solid collegial relations with faculty, and participate as much as possible in the "academic profession". Because after research (ideally published) you'll need three LORs for your grad applications - and you want to give your professors every opportunity to remember you as a capable, enthusiastic, and personable student who will be a credit to any program.
Now, obviously, a huge public university like UM will likely have many more opportunities for this sort of thing, but the advantage of a small school is that you don't have to fight your way through hordes of sweaty teenagers to score an office hours meeting with a real professor.
And of course, the lower stress level of having what sounds like a free ride at Eastern, especially with your family responsibilities, is nothing to be sneezed at.
Finally, there are a couple good books about grad school that may provide a bit of perspective:
Getting What you Came For, Robert Peters
Graduate Study for the Twenty-First Century, Gregory M. Colon Semenza
The first one is hopelessly out of date in terms of technology, but both will provide a lot of insight on both grad admissions and how to survive once admitted.
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