I followed this guide:
Start with upgrading and removing dice, saving the "get new die" option for later if possible, since the quality of dice you get from that goes up the later you get. I tend to grab upgrades on an attack die and a block die early, while my first removal is one of the three boost dice. Don't upgrade the heal die at all, you want to eventually replace it with a Hollow if anything, though you can get by without if you get your deck quality up early. I try to end up with 1x gold attack, 1x gold defense, 2x silver boost, and 1x normal mirror die or 1x gold hollow mirror die. You CAN get 2x mirror dice, and that's fine but you have to make sure your deck is pared down if you don't want to get stuck with a bad hand. Gold booster dice are not good since they can roll 4, which is bad for the mirror dice.
Other than the core 5, I usually will end up with some mixture of:
1x heavy block die, silver or higher
1x hollow booster die, silver
1x hollow attack die, silver or higher
1x healing die, hollow or Miracle
Check out the dice wiki article for info on special dice