Wizards are the kings of direct damages, be it single target to point blank area of effect (PBAE or around the caster), no one shine as they do when it comes to hitting a target to the ground as fast as possible.
They use to be also the best transportation system with druids before PoP and PoK stones, but this side of the job here on Lazarus get even less utility as Valium will port you almost anywhere you want. The only mention is for "translocate: group" which allow you to send all your group to their bind point.
Solo: As much as I like playing a Wizard, playing solo is pretty boring. Root, nuke to death, root, nuke to death. Things get a little more interesting past 51 when you get atol's spectral shackles so you can snare a pack of 4 and nuke them 4 with your targeted AoE, then snare an other 4 pack and nuke,...
Melee Group: As a DPS class, wizard can easily be plugged in a melee group. But melee group will tend to take Shaman over Druid and the 25/35% spell dmg aura of the Druid will really miss. You're also really mana dependent and tend to burn it fast, so without a class who can help you regen your mana expect a lot of med time. Kerafyrm's Prismatic Familiar will be mandatory to achieve high dmg, as you'll probably miss Druid aura.
Caster Group: 3 classes benefit strongly to wizards, and they are generally found in casters groups. Druid, as they get a +25/35% spell dmg aura (lvl 55/65), Bard as they help regenerate mana faster and get spell dmg boost song and enchanter as they got mana regen buffs and more important, dual cast aura. And those are generally found in casters groups. As an exception, it's not Wizard who make this group shine, but the caster group who make Wizards shine.
AoE Group an other essential part of the AoE groups is you, if nobody can take enchanter's place at stun locking, others can do the PBAE damaging, but none will do it faster than you, you can start early on, in fact, from lvl 20 when enchanter get their 2nd PBAE Stun with some heal. But wait for the Jyl line of spells at 53+ to really shine and make short work of pack of mobs.
The most difficult thing to do as a Wizard, is managing your aggro.Doing damage is nice, but having only cloth to protect and making hard and fast damage, means you're going to get your tank a hard time and consume your healers mana faster until they have solid aggro AA. Paladin or Cleric can easily prevent this by blinding mobs. The other way is to set a /noAggro after your Nukes spells. Concussion line of spell lower also your aggro so setting up a
Main=Ancient: Greater Concussion/PctAggro|80 Main=Claw of Frost/noAggro
Should allow you to prevent getting unwanted aggro. (Keep in mind that your elemental pants "Maelin's Leggings of Lore" have Concussion clicky for free, from any slot and can be casted during recast delay)
Your spells lines are pretty easy, frost spell are usually fast cast low damage spells, fire spells hard damage long cast, magic seems to be less resisted. Bolt use to have longer range, Lure are the low resist line, pillar the targeted AE (limited to 4 target) and we have PBAE (around the caster, without target limitation). Be aware that the targeted AE can harm you if you get inside the AE range.
Remember to set Harvest in your ini and put it on a gem you won't use, cause the recast time is long and you'll get a nice mana regen. (only downside, it'll stun you for 10s)
Wizard is really straightforward class, you do damage and want to improve it.
Force of Will → Mana free DD each 20 seconds (up to 14 sec with hastened Force of will) start with a raw 950 dmg (lvl 1) to 2150 dmg (lvl 7).
Spell Casting Fury improve your crit chance and damage.
Spell Casting Fury Mastery improve more your crit chance.
Destructive Fury same for crit damage.
Spell Casting Mastery less spell mana cost means more cast.
Arcomancy/Cryomancy/Pyromancy they all boost damage done by spells made on your target (magic/frost/fire)
Improved Familiar An improved version of your Familiar and for a really cheap cost(Kerafyrm Prismatic Familiar is better and will allow you to get rid of your Druid Aura as it gives you 40% dmg and a 10% crit chance bonus at max AA, but the Druid Aura won't stack with it, and the AA cost to get it is heavy).
Spell Casting subtlety dual casting up to 2x30k dmg on Quarm (for a really well geared and with a lot of AA Wizard) can be pretty challenging, so making less aggro is always nice.
Combat agility/shield block/staff block avoiding hits is always nice for a caster, not as critical as for our Enchanter Brothers, but always nice when you wait for the tank to get aggro back after your last critic record.
As most Casters try to find heavy focus gear. Best focus are Mana cost reduction, damage augmentation and casting time reduction.
Elemental silk armor is a good bet as it got a lot of focus and decent stats.