I use Dominion Shuffle for Android, full random.
Dominion Shuffle automatically calculates whether the game should have Colonies or Shelters.
Usually, after each game, we take turns to pick a card to keep and a card to remove, starting with the winner.
The cards that players before you have chosen to keep can't be removed (and vice versa).
We also usually remove any stack that ran out (other than the base cards, obviously).
Dominion Shuffle has a handy feature where you can remove individual cards from the shuffle, so those we have already removed don't come back in.
This means we have plenty of variety without having to replace all ten stacks every game.
It also gives players a little bit of control over keeping cards they love/vetoing cards they hate, without completely removing cards from circulation like a pre-game veto does.
Given that I'm usually the one who owns the Dominion sets, I usually just handpick the cards I want to show off or play with.
Man, I seriously hope you're not like that guy who plays the same kingdom over and over so that he can thrash newbies.