Jackson's backcountry is kinda scary right now (or at least while i was there during christmas) cuz of the weird snowpack. alot of avalanches happened earlier this year so idk if the backcountry is safe right now but if it is hit that shit up.
in-bounds the alta chutes, tower three, and the toilet bowl are favorites of mine. the expert chutes are also great.
there is tons of good stuff all over the place, u shouldn't have trouble finding it.
the people are super nice too
as for what to bring, i'd bring what you'd normally bring on a ski trip (clothes for on and off the hill, toothbrush etc.) also it might be smart to invest in a backpack
great place, Jackson
have fun