You might consider starting light(er) and doing power cleans. Add some weight. Repeat. When those get tough, go to high pulls. When those get tough, go to low pulls ("power shrug starting from floor"). When those get tough, deadlift.
Or, just do some power cleans to warm up. Or, let various "slam pickups" be your explosive hip lifting and do the DLs in the gym.
To answer your "one or the other question" we need to know what you are good at (weaknesses?) and your mma style. Are you (or the person in question) a strength athlete already? If you are a true mma beginner, you might become a striker, ground 'n pound, submission, etc. For getting people to the ground (possibly by picking them up first), I like power cleans. For dominating people while on the ground, I like deadlifts.