Q: To change the Goal, do I just stack a new Goal on top of the old one?

A: As the rule sheet states in the section describing the different types of cards:
“To play a Goal, place it face up in the middle of the table, discarding the previous Goal, if any.”

You’re not supposed to just stack up the Goals on the table. The old ones should always go in the discard. That said, it happens quite frequently that people play a little “lazy” and stack them for a couple of turns, and then suddenly someone remembers that those should be in the discard, and cleans it all up.

There are very few cards in Fluxx that allow or require you to pull a Goal out of the trash or for which the exact order of discard matters, but there are a few, so you should just get in the habit of making sure you discard the old Goal whenever a new one is played.