All skills can be bought with gold, so there's no real point in having a skill set until very late in the game.
You'll find that the most useful wizard skill will be ice arrow, because of its fast cast and cooldown. Mob control skills such as scorching strike, icy grip, and magic star cannon will also be very useful. Also don't forget instant recollection (cast speed) and astral surge (mcrit)
Safe return will also help.
Magic Shackles, prison of dancing blades, Absolute Zero, and magnetic charge, teleport, and will melter(-mdef) forward will serve you well in PVP.
Once you become an archmage, Chain Lightning Arrow's double attack makes it the predominant DPS spell instead of ice arrow, huge toxic cloud becomes usable in pvp against stealth, and high mana shield is basic for survival.
PVE wise, you will be loved in parties if you buy burning veil.