Amalloy, you identified the correct strategy, but slipped a bit in the execution.
I do agree with your opening: Watchtower/Potion. Watchtower actually combos specifically with University (it's one of those cool advanced player tricks). Having Watchtower and University in hand allows you to top-deck the Actions you are gaining, and then play Watchtower to draw them.
You are going to want tons of Actions, Actions, and more Actions. Watchtower is good (it's you cheapest option, and does the combo). Library actually goes really well with University, too, but Council Room has the all important +buy.
Watchtower, Library, and Council Room are all terminals, so you may wish to add Golems to your deck at some point so you can play your terminal Actions.
You probably will have a powerful deck that can turn for Provinces at some point, but hold off! The Vineyards are way, way more important. Think of them as your own personal Victory Points pile. You want lots of them--leave your opponents to fight over the increasingly difficulty to purchase Provinces. You probably can't get your Vineyards to be worth as much as Provinces, but you can still make them worth a lot of money. Tons of Actions (Universities, Watchtowers, Council Rooms and Golem), Vineyards, and maybe a few Provinces, make the winning deck here.
Apprentice isn't so hot because you don't actually want to trash your Actions, although trashing like a Golem or something gives you really good non-terminal draw, which could allow you to play more Universities... there may be a point at which you would prefer to add Apprentice over other things, but it's tricky.