So after a few subjective years, you will be overtaken by newer and faster ships, and when you arrive, there will be a flourishing civilization already there to greet you.
Meh. People were willing to go half-way across the world to try living somewhere new, probably never to return. Announce the trip, and you'll have to weed out volunteers pretty viciously.
I agree that the real problem is fuel, but 10 years isn't quite long enough if you are going to accelerate halfway and decelerate halfway to arrive at low speed. For a 2,500 light year trip composed of two 1,250 light year legs, the time experienced by the ship will be (in units where c and a are both approximately 1):