If I'm taking things very seriously, Attacks/trashing/+buy/villages, and just cards I know to be good (AdamH's list is a good starting point, available
here).
Then I see if any cards go nicely together. If there's an interaction that isn't immediately obvious that I notice, there's a chance my opponent didn't and that may give me the edge to win the game.
In general though I just look for what I think will be a good opening. I had a pretty good working knowledge of what the strong openings were back in the Isotropic days and the habit never left me. It's more of a cursory glance at the rest of the kingdom with the above in mind than a proper checklist. I'm more likely to go through the above process waiting between turns than at the beginning, and my opponents choices often spur on thinking. Not even sure I play that much better when I spend a long time looking at the kingdom before buying my first card (that's not advice, that's just my experience).