Alrighty, let's get started here. You're a necromancer, wonderful pick very fun class.
Spells you should always have: Basically, all your up to date level spells, and quest spells you can pick up along the way.
Your pets, are a NEED at all times that you plan to be killing. They will save your life always, they usually do a good job at holding aggro (Where they keep the mob off you while you nuke the crap out of it) They do good damage and they can take quite a beating. At the early levels, you'll find your pet to be slightly weak, but is as to be expected, it's low level, you're not that strong yet, as you progress your pet will probably get stronger than you for a little while, Be sure to have it out at ALL times, and always use your most recent pet, the Level 8 pet will be superior in every way from your level 1, it will have more health, do more damage, and take less damage.
Personally, I'm not a Necromancer, but I am a Magician. The concept is the same, only, a lot different. o.o Makes no sense, but just keep using your most up-to-date spells and you should be well off and all set to level your way happily to 60.