Dominion is a great game. The game plays like ascension, but has a more strategic element, since you don't get screwed by the changing cards available on the board. In Ascension, you basically make one decision: "Fight or Buy", and you try to focus on that build for the rest of the game. In Dominion, every turn requires quite a bit of thought, if you're trying to maximize your gains.
I've been thinking about the strategy of Dominion in terms of what to do in the first two turns.
First of all, the first two turns are interchangeable. If you buy card X in turn one and card Y turn two, your deck will be the exact same when you shuffle your 12 cards as if you bought card Y first and X second.
You want to start off with two cards that do something directly. No cards that simply help another card in the first two turns.
It's difficult to figure out the correct ratio between action cards that do things, and action cards that support playing more cards. A lot of it depends on how many cards give +2 actions.
If you can buy a gold or a Province, get it every time.
One last thing: Don't be afraid to buy silver in the first two turns. Your main goal in the game is to buy expensive things, and starting early works great.
I forgot the best part! This site has a random dominion starting generator. If you play Dominion, it makes for a lot of cool variety.