Two you should consider, even though rated M.
Diablo 3 might be rated M, but the gameplay is so high up you really don't see gore and such. I do believe there is one level with a succubus, but never saw any detail. Played through the non expansion one with kids and it seemed fine.
Halo 1-4 is one of those games that should have been rated T for Teen. Great FPS without all the Call of Duty language, content, etc. They just released that full collection on Xbox One, would have to single play each one for Xbox 360, and Halo 2 is still OLD Xbox format, but runs on Xbox 360.