End of Campaign?

First off, love this game. Got it on Steam and the game design is very well thought out!

I just made it to the mission with a bunch of rotating to rings, where you can access the arcade and scenarios. I clicked on the third node, which looked like it had several options between "trench run" and destroying turrets.

I clicked on the trench selection, and it brought me back to the opening cinematic with difficulty selection. I was trying to get zarix's (sp?) inheritance...did I do something wrong?

If you haven't gotten Zarix' present yet, you need to scroll down all the way to the bottom.
If you've already gotten it, then proceed to the next part of the campaign - this is where the game really gets going! Look for the next Galaxy at a theta of roughly 3.5. What this essentially means is GO LEFT on the Galaxy screen.

Thanks man, your reply is helpful.

So I guess what I'm confused about now, is that I think my campaign started over. Is there a way to go back to that Galaxy screen, or do I have to play through the campaign all the way to get there again?

I usually click "continue campaign", although my friend just told me that we can select missions individually too (duh!). Maybe I'll take a closer look at that.

tl;dr Not sure if there was glitch causing me to restart campaign, or I just failed.

You'll want the Mission select/Galaxy map screen. Your friend indeed knows what he's talking about.
Occasionally the game will put you into that screen to select your next destination, but mostly, you'll have to get there yourself.