A combat focused Factotum might benefit from choosing Divine. The standard cleric buffs would probably be enough to turn him into a combat monster, just as they do for the cleric. Especially if you can swing some kind of Persist trick. Guidance of the Avatar or Divine Insight would pump his skills through the roof if there was some check that he really, really needed to make.
I can't really think of any reason for him to choose Psionic. He doesn't have enough uses/day for the action economy tricks, and I can't think of any specific powers that would be useful for a Factotum that Arcane or Divine can't replicate. I guess it would be kind of nifty in that PLAs scale for free according to your hit dice, so your low level powers would be just as useful as your high level ones.
