Compound movements are much better for strength training and typically translate well into MMA since they'll build functional strength and most of the big lifts will involve the core to at least some degree. Bench press, squats, deadlifts, standing overhead presses, bent rows, power cleans, ect, are all good. I'm a big fan of Rippetoe style weight training routines to maximize strength gains.
Bodyweight exercises are good for upping your endurance as long as you're doing something other than just your generic pushups and situps, along with anaerobic cardio to improve your conditioning even more - short, difficult exercises like sprints, intervals, burpees, ect - and plyometrics for speed.
It's tough to work everything in effectively - lifting, cardio, bodyweight, plyometrics, technique training - but it can be done.
"I don't want them to like me, because when I'm in the ring, punches fly to the face. It is not a tenderness time. I am not falling in love. And he knows that when the fight starts I am kicking faces."
- Wanderlei Silva