If I just leave them as is, what happens?
Nothing, if a fork occurs, you get coins on the two sides of it.
If I switch my Trezor to UASF, what happens?
If you do not spend your coins after a fork happens, nothing happens. If you spend coins after the fork, you might expose yourself to replay attacks even though you are transacting on the UASF chain. That means your transaction on the UASF chain might also happen on the other chain without you intending to. You can find more information about replay attacks here.
Do I get coins from both chains? Do I need to pick one before August 1st?
You'll get coins from both chains for all the coins you have before the split occurs. If you buy coins after the split, you'll only get coins from the chain you bought them on.