My girlfriend and I played this at gencon and we absolutely loved it. Is there a team we can make in one core set that's does really well, or should we just stick with the starter decks?

you wont have a whole lot of options to tweak beyond the starter decks with 1 core set. That said, I think Roland/Wendy is pretty good. I would say that's the best 1 core set team. You'll probably tweak the starter deck slightly, It seems natural to take Wendy's copies of Overpower and give them to Roland, and take Roland's Manual Dexterity and give it to Wendy. That's a good place to start.

I would agree, you need someone 'good' at getting clues and someone good at fighting. As a combo they have the best chance to beat the agenda deck. It's natrually not impossible if you want to pick other characters (I first did the campaign with Roland and Agnes) but we did stutter at some points due to lack of natural clue ability (I wont say how it ended but lets just assume bad things happened), just re-completing with Roland, Wendy and Skids and it has gone extremely well so far (cant say how without spoilers)

I think as long as you were playing on Standard that Skids + Daisy would not be bad. Daisy's high base intellect means she is pretty immune to card inconsistency... except you may wish to proxy one additional Old Book of Lore. There are plenty of weapons for Skids to take, and generally any pair with a seeker is going to do better than a pair without a seeker.

You basically want to stay away from Agnes if you have a single core. She is very inconsistent without a second core.