Train your legs for power and stability - squats and deadlifts, but also use plyometrics - like box jumps, jump squats, etc. As for the upper body, you should also train for power and stability...use dumbbells instead of bars and stay away from machine-based exercises if possible! Full body workouts are the best. Use a varying range of reps for your workouts - monday 3 sets of 8 reps, wednesday 4 sets of 6 reps...etc. I use a factor of 24 when desiging my workouts - 6x4, 4x6, 2x12, etc...each day I use a different set/rep scheme.
The 'core' muscles can be trained at anytime, using any exercise - and they don't have to be 'ab' or 'core' specific moves. However, some golf specific core moves I like are wood chops, seated med ball rotations, seated med ball rotations with throw, and swiss ball lower body rotators.
Don't forget to train your forearms and grip!!! A good strong grip is essential!