I lived in Lexington Park and moved because the schools there are horrible. We moved north to Mechanicsville and the schools were much, much, better! I can't say that all of the drug activity in the county is in LP, but I can say that its most visible aspects are there. Mechanicsville also puts you about even distances between work in Lexington Park and shopping in Waldorf. Having to drive 90 miles round trip to go to a mall was a bit much when we lived in LP.
Country Lakes is nice, but you've got to do some driving to get anything as there are no stores that are very near. Not a problem for some, but I would never want to make a 20-mile trip to get a hamburger. I lived in the Golden Beach area, and I was five miles from everything I could want.
Traffic is bad in Lexington Park proper, but once you get past Wildwood to the north, or south of the base, it gets much better. Calvert County is nice but you do have to deal with bridge traffic, which goes from bad to hideous if there's an accident on RT 4.
When I moved out of the area last year there was still a big shortage of rental property in the area, and I don't know if that's still the case... probably is though. The short supply of rentals makes getting a short-term rental difficult, but there are extended stay hotels and some short-term apartments in LP. Since kids aren't an issue at this point my suggestion would be to start at the Extended Stay America, which is all of a mile from the base gate, and use that as a base of operations until you find some short-term housing. But if you're going to have kids I would definately suggest looking at the northern part (mechanicsville) of the county for a permanent home.