As a Death school wizard you have the unique ability of healing while attacking, which usually is more than capable of sustaining you while you progress through the Spiral. As you level you will notice more attack spells, but others that allow you to manipulate your enemy's damage, and even temporarily force some enemies to fight for you.
Level 20s I suggest you visit the Balance school tree, Niles, in Krokotopia for Spirit Blade to boost your damage.
Choose a wand from a different school so it won't prematurely use your Death school damage blades.
The trainor Mildred Farseer in Colossus Blvd. offers you another Balance spell, Reshuffle, and may prove useful to you in certain situations.
Diego in Unicorn Way offers you Stun Block, which you may desire in your later levels.
Focus on acquiring good gear through the Bazaar, gear drops, and Crafting, while attempting to train a beneficial pet. Use your spell deck wisely, and don't feel the need to place every spell trying to anticipate every situation.
Don't rush in to using your Training Points as soon as you get them, because as you level and experience more difficult content, your needs will change.
"Don't rush in to using your Training Points as soon as you get them, because as you level and experience more difficult content, your needs will change."
This ^ I'd also advise against training Ice spells if you don't PvP. Tower shield is a must-have in the arena, but not often needed for questing, and easy to get as a Treasure card for the very few times you'd want it.
Balance for the Spirit Blades, and Life for the heals. Death is a good school for supporting others so Life and Death would go nicely together. It's also good standalone school that can do huge amounts of damage, so it's well-balanced.
Oh, and don't forget Star and Sun spells when you get to Celestia. Those are super handy.