So my pathfinders group is running a campaign next semester where we'll take turns DMing, but keep our characters between sessions. I volunteered to be first because yolo. So, my question is, since I'll be DMing for a 4 hour session, should I try to do a single story, or should I try to do a single cohesive story, or just give the party a couple different miniquests to mess around with?

I suggest you adopt an "episodic TV series" structure where each session has a self-contained story. That way you don't trip over each other while trying to GM. For example, you could have the party be a group of explorers in distant lands, or they could be tomb raiders, or they could be some sort of company for hire. Once some supporting characters have been established, story arcs will form on their own.

The most inoffensive way to do session 1 would probably be a relatively simple dungeon crawl. You should be able to get the hook for, get to, and hack through a den of evil in about four hours real time.

Overall, though, you could totally think about weaving in a meta-plot. I do think CKY has the right idea with "episodic TV show" -- not every episode of X Files or Stargate SG-1 has the show's arc/season's big bad involved, neither should every session in a game like this, and you can leave off developing one until you see more of what your compatriots do.

So, what did you decide to do?

~SE++