When doing PBF games, I'll stack the decks to keep the cards straight: Cards in play face-up on top, then the character card, then cards in hand face-up, then the deck face-down, then the trash face-up. If you do that, the only other thing you need is the HP totals and to remember what effects are active.
What he said, trash face up inder the deck(s). Character cards and hands on top of the deck face up. Any charging cards face down under the weapon or whatever is being charged. Then all that is needed is to record the hits everyone has taken and any buffs or nerfs they are affected by.