Sorry if this is a question asked a lot, I've spent a few hours researching this on a few websites and have come up with little.

My rule question is: If more than one event is triggered at the same time, are you allowed (the first player) to decide which occurs first?

My guess is yes, I'm just looking for confirmation.

Example game I played tonight: Playing base game + Innsmouth

In this game the Deep Ones Rising track is at 5, and Mandy's personal story is at 4 clue tokens. Mythos Phase the gate hits a seal, triggering both the Deep Ones to awaken Hastur (I'll likely loose with current setup) and Mandy's story to complete, allowing her to seal a gate (in this case the only gate left on the board, and there were more then enough trophies to go around), causing victory condition. I assume I'm allowed to pick which happens first, correct?

This paragraph is in the original rulebook, so I guess you win:

"If two or more game effects happen simultaneously, the
players choose the order in which they occur. If the
players cannot agree, the first player decides."

Yes, you the players decided how the instances are resolved (and if the players can't decide, the First Plauer chooses). The same thing happens with Wendy's Personal Story as well, because she needs there to be so many Elder Sign tokens on the board, but cannot give up her Elder sign without gfailing, so if she uses her own Elder sign, she chooses whether or not she passes or fails her own Personal Story. I'm pretty sure this is clarified somewhere official, either in an FAQ but I think I read it in an answer from Kevin...