I'm trying to understand what you mean in the first part of your message -- that "the first one won't start until approx. 1pm after airport arrival." Are you just trying to figure out whether you should just do Animal Kingdom w/FP+ for the Jungle Book show on your arrival day or if you should do it on a different day but, but want advice on what park to do with stand-by in the morning on a different day? If that's the case, I think the park that the crowds build the slowest in the morning would be Magic Kingdom -- so you could do the "most" there without FP+.
Having said that, I love Animal Kingdom and think there is a lot to do there that doesn't require any wait time...so by hitting a few headliners at rope drop (i.e. Safari, EE, Dinosaur), you could then spend a few hours just doing shows (Lion King, Nemo, Flights of Wonder) and walking the different trails, checking out Harambe Market, checking out planet watch, etc. and then use your FP+ for a few things in the late afternoon/evening.