There are 2 variants of spells: the elemental ones and the stardust ones.
Both require you to invest in them, so I recommend going with only one route.
Elemental Spells
Arcane Armor
A decent defensive tool that, while chanting, gives you increased physical damage reduction and reduces the movement of any enemy that hits you
Cryptic Ward
A Block that negates all damage, best used as a parry cause it knocks them back that way.
Crystal Icebolt
Summons 2 icebolts on each shoulder that will fire at an enemy that hits you; will also automatically fire when the duration expires—good defensive tool to keep enemies away from you.
Deep Freeze
Very good CC that shoots a wave of frost in a cone in front of you, which both deals damage and slows enemies hit.
Elemental Affinity
A passive that applies a stack on enemies whenever they are hit by elemental magic; if they have 2 stack can be used to explode the stacks, dealing damage.
Eye of Insight
After chanting, scans a large area for players but only has a limited use. Better in trios than solos.
Fire Bolt
Fires a short-ranged fire bolt that can be charged to deal increased damage. When it hits an enemy or the floor, it explodes, dealing damage and applying a short burn to the target.
Flameblade
A melee slash that deals damage and applies burn to the target.
Forbidden Gate
Places down a wall that blocks enemies and their projectiles from passing through. Allied projectiles go right through it. The wall can be destroyed if enough damage is done to it.
Gravitational Vortex
Summons a vortex at the target location, pulling enemies in after a short delay, dealing magic damage; if more than 1 person was hit, it stuns them. Not so good in solo, insanely good in trios.
Meteor Charm
After a short chant, fires a meteor at the target location, dealing magic damage. It can be cast early to deal reduced damage.
Meteor Impact
Shoots multiple meteors forward, knocking up any enemy hit while dealing damage. The meteors shatter upon impacting an obstacle or enemy.
Mistwalk
You enter mistmode where you are unaffected by anything. You do have reduced movement speed and are prohibited from certain actions like dodging.
Phantom Step
After a short chant, you get increased movement speed, and your footsteps turn silent. During
Phantom Step you also take no fall damage or stage from falling.
Rockblast
After chanting for a short while, gathers rocks at the target location, which explode after a short delay.
Shadow Veil
After chanting, you enter stealth for a duration. Energy does not regenerate while stealthed.
Star Shock
Expand a ring outward which deals damage and knocks back enemies hit.
Thunderstorm Sigil
After a short chant, a sigil is placed at the target location, which is shortly thereafter hit by a thunderstorm, stunning and dealing damage to enemies.
Thunderstrike
After a chant, release a thunderstrike at the target location. If released early deals reduced damage.
Windcraft
Summons a tornado which, after a short delay, moves forward, damaging and knocking back enemies.
Stardust Spells
Stardust Energy
Passive that greatly increases movement speed while chanting and makes stardust magic damage regenerate energy.
Stardust Tempest
Summons a tempest after a shot chant at the target location, dealing damage and slowing enemies.
Stardust Torrent
Hold to chant; after chanting, you summon a torrent which you then guide towards the target direction, dealing damage. The torrent becomes stronger the longer it travels.
What skills to take when
What you take really depends on what you want to do. Personally, I will go with my fire/ice setup, which I really like. You have 6 ability slots as a sorcerer:
Fire Bolt as your main damage tool
Flameblade for anybody who comes close
Deep Freeze as CC when you want to disengage
Crystal Icebolt for any enemy that does hit you
Shadow Veil to move around, especially in solo mode
Elemental Affinity as a finisher when you already hit them with magic.