Fenwaysouth,
The NCAA pays for all teams that make it to post-season. They pay for hotels, meals, and TRAVEL (Airfare).
They choose the regionals months in advance because the NCAA loses money on D3 and D2 tournaments. They want to keep the teams as regionally based as possible so they don't have to fly teams all around the country like Division 1 does. The D1 regional sites (UVA, UNC, USC, Vandy, Cal State-F etc.) are awesome stadiums that can host as well.
Some D3 schools don't have the facilities to host. Shenandoah for example does not have the facility to host because of poor lights and a terrible playing surface (From experience- my face stills has scars). CNU has everything needed but can't host because they don't have lights. D3 regionals usually have 6, 7, or 8 teams as with D1 having 4 teams in the regional and a best of 3 super regional.
Most D3 teams that host have use local minor league staidums or have facilities with lights, great playing surfaces, ample seating/parking
Hope that clears it up. That's as best as I can explain it.
Great site www.d3baseball.com
Has all you need to know about NCAA Division 3 baseball.