It isn't THAT BAD, but it isn't great either. It has room for improvement. I remember I'd would pass by part of Compton, and there were some really nice houses there. So it isn't all that bad in my opinion, but there is crime there. I'm not sure how "race" will play a role.
You may want to consider moving to Carson, it is much safer and close by Compton.
You should check these links out for crime information and more.
Compton
Overall information
http://projects.latimes.com/mapping-la/neighborhoods/neighborhood/compton/
http://www.cityrating.com/citycrime.asp?city=Compton&state=CA
http://projects.latimes.com/mapping-la/neighborhoods/neighborhood/compton/crime/
School information
http://projects.latimes.com/mapping-la/neighborhoods/neighborhood/compton/schools/
Comments on Compton
http://projects.latimes.com/mapping-la/neighborhoods/neighborhood/compton/comments/
Carson
http://projects.latimes.com/mapping-la/neighborhoods/neighborhood/carson/crime/
Overall information
http://projects.latimes.com/mapping-la/neighborhoods/neighborhood/carson/
School information
http://projects.latimes.com/mapping-la/neighborhoods/neighborhood/carson/schools/
Hope it helps, I live in South L.A. (another bad neighborhood) and I hear Compton has improved, but it has ways to go.