I grew up in Springfield, VA in a military family, so I'm very familiar with Ft. Belvoir and that entire region. My dad was in the Marines and worked at Marine Corp headquarters, but Ft. Belvoir was the closest commissary and military hospital, so we went there often.
First off, Ft. Belvoir is in Fairfax County, which is good, but this is the worst part of the county (southern Fairfax). The whole Route 1 corridor is just an ugly area in comparison to the better parts of the county. Hybla Valley is especially bad. I wouldn't call it dangerous, but I certainly wouldn't want to live there.
You mentioned West Springfield and that is the better part of Springfield. Springfield has changed a LOT since I grew up there in the 80's. The worst part of Springfield is the central part near the mall. I personally wouldn't live in central Springfield today. While Fairfax County has some of the best schools in the nation, they are not found in Central Springfield. The place is completely overrun with ESOL students. West Springfield has fared better and West Springfield High School is much better than some of the other Springfield area high schools (stay away from Robert E. Lee, Edison, Hayfield).
Burke is safe and has decent demographics. I would say Lake Braddock is a better high school too. The only issue is it's densely packed with townhouses and there is really nothing else there.
The better parts of Fairfax County are found mostly in the western areas (Chantilly, Reston, Oak Hill, Vienna, Oakton, etc.).
You should definitely visit before buying a house here. Personally, I wouldn't want to stay longer than necessary. I dream of moving almost daily, but my wife and I are heavily tied to the area. Without those ties, I would be out of here.
P.S.- Stay away from even crappier areas south of Ft. Belvoir. Lorton, Woodbridge, Dale City (yuck!), basically all of Prince William County is off limits. And don't even think for one second looking across the Woodrow Wilson into PG county.
John