…For example, if one card would make me win, but playing another would undo or prevent it, can I just play the card that makes me win and stop there, or do I have to play all of the cards, negating the win?
A: For As long as the negating card is not a Creeper (see this question) you can play the card which would make you win, and the game would end (assuming it’s not stopped by a Surprise, of course). For Actions and Free Actions which involve the playing of multiple other cards as a sort of subroutine, you CAN win from one of those cards without needing to play them all.
Cards which create “subroutines” of the execution of other cards:
Actions:
Draw 2 & Use ‘Em
Draw 3, Play 2 of Them
Fizzbin (Star Trek)
Taskmaster (Remixx, More Packs)
Do a Trick! (Dog)
“Free Action” Rules:
Goal Bonanza (Remixx, Astronomy, More Packs)
It’s a Quest! (Black Knight expansion)
“Free Action” Meta Rule:
5-Card Mission