What are your academic goals and interests? What can you afford, and can you get financial aid for academics and/or athletics (latter D2 or D3). Those should be your first questions. The type of school and athletics program are usually secondary.
There is a lot--like a ton--of snobbery here on letsrun. You have to be D1 or Ivy League, or you are a nobody in their book. But they are nothing but a bunch of preening peacocks and pay them no mind.
It's worth your while to look a spectrum of opportunities. As a scholarship athlete you do what the coaches ask and what the program requires. D3 do have some very solid teams and programs, but at those you are more of a student-athlete and your academics generally outweigh what you are doing for your team, like if you have a lab or field trip the coach is going to defer to that, whereas a D1 coach would be more likely to say, my way or the highway.
Obviously the level of competition is much better at D1, but find out what the coach and team at a particular school are like.
And yes, D3 schools do sometimes compete at big time meets in XC and track. It just depends. However, I've seen D3 schools line up at Stanford or Sundodger on the West Coast, and places like UW also have indoor meets with runners from all divisions. Likewise, Drake or Penn Relays take runners from all divisions and entry is based on performance, not prestige of the program.