I take warming up very seriously on lower body days. I used to jog a little, but found it didn't help much. I do plenty of mobility stuff and bodyweight lunges to loosen up my hips, which have been giving me issues lately. I don't spend a lot of time on it, but I still take it seriously.
As for upper body stuff its more just some arm circles to get the blood flowing.
Current PRs at 242- 495, 345, 585, 1425