In arena battle you want as many shields and blades as possible with a few heals and one or two of your own heavy hit spells and perhaps two smaller ones. Your treasure card side-board should be loaded with heavy hits from your school's spells (for lower pip usage) and a couple from other schools as a surprise for your duelist who you are trying to kill. You should have one ice, one storm, death, fire and life if possible. The advice that was given to me, that seems to bear out is, have a couple minion cards and use them as often as possible to do general attacking.
One last thing for Arena battling is the essential Reshuffle card, or two, or three, in your treasure card sideboard. These help you recycle your cards in the event you throw away a good spell or the battle is going for a long time and you're running out.
For street battle you will want to coordinate with your friends and put as many multi-strike spells in your deck as you can fit along with blades and a moderate number of shields and a couple healing cards. With a couple friends and a few multi-strikes there's no street battle too hard. Keep your treasure cards set with a different school's multi-strike, one heavy hit and an extra healing card or two just in case.
Balance your deck with about 15% blades, 5% traps, 30% shields, 10% multi-strike, 20% heavy hits, 5% heals, 5% small strikes, 10% miscleaneous. Your treasure cards should include only perhaps three heavy strikes and two heals. (But don't forget to build them up after each battle) Having a small set of treasure cards ensures that you can draw what you want within one pass of card-play.
Treasure Card Treasures
You should visit your ice friends and get a steal, freeze a colossus and multi-strike like Frost Giant. From fire you'll want a Link and Choke along with a Fire Dragon and Phoenix. From storm you'll want a couple Wild Bolts, Triton and Storm Lord. From Death you'll want a Scarecrow, and a Vampire or Wraith. From Life you'll want a Regenerate and Centaur. From Myth you'll want an Authoros and Humongofrog as well as a Minotaur.
Yeah, there's more but I'm not going to give up too many secrets in case I meet you in the arena!