With the introduction of toggles, you have to use all 3 of Rift Mage's spells to get the most out of the specialization.
I use Veilstrike as a cooldown reducer or as a weakness inducer.
I use Stonefist as a guard damager or a weakness inducer.
I use Pull of the Abyss strictly as an area of affect damage dealer.
So when there are no enemies with guard, I use Veilstrike for spell cooldown, Stonefist for weakness and Pull of the Abyss for damage. When there are enemies with guard, I use Veilstrike for weakness, Stonefist for guard and Pull of the Abyss for damage.
Now for spells, I will go over each school.
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For Inferno, all spells except Flashfire is fair game. Whichever one you want to use is up to you.
Immolate is the most cost effective spell. The alternate upgrade for Immolate makes it practically spammable.
Fire Mine is the most damaging spell. Flaming Array upgrade for Fire Mine turns it into a powerful defensive spell for a Rift Mage.
Wall of Fire is the spell with the most utility. I am not sure what the alternate upgrade for Wall of Fire does though.
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For Winter, I would suggest picking between Fade Step, Winter's Grasp and Blizzard. Fade Step gives you mobility or free mana. Winter's Grasp gives you crowd control or high single target damage. Blizzard gives you area of effect, crowd control and damage over time. If you wish to pick Blizzard, I recommend sticking with the Ice Storm upgrade over Winter Winds.
Blizzard with Winter Winds - 75% weapon damage per second, 10 seconds duration, 8 meters area of effect, 8 seconds chill, 24 seconds cooldown, 40 mana cost. Blizzard with Ice Storm - 150% weapon damage per second, 8 meters area of effect, 8 seconds chill, 4 seconds freeze, 24 seconds cooldown, 5 mana per second cost.
This means that Blizzard with Winter Winds does a maximum of 750% weapon damage for 10 seconds with a mana cost of 40. For 40 mana, Blizzard with Ice Storm will do 1200% weapon damage for 8 seconds. For 10 seconds, Blizzard with Ice Storm will do 1500% weapon damage with a mana cost of 50. To achieve 750% weapon damage, Blizzard with Ice Storm only needs to last for 5 seconds and cost a mere 25 mana.
The reality is that Blizzard with Ice Storm is still the way to go if you wish to use Blizzard. In my opinion, Winter Winds is the Blizzard upgrade for AI because it makes Blizzard into a weaker fire & forget spell.
Many would advise against using Blizzard but I find that if you play it right, Rift Mage is the only mage specialization that can sustain Blizzard long enough to do any real damage.
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For Storm, all the spell in this tree are fair game. You have to be careful about your upgrade choices though. Like other posters warned, many Storm spells can cause the Sleep - Weakness bug. Whether you want to exploit that or avoid that is up to you.
Chain Lightning is a good early game spell and you can go with any of the upgrades. Energy Barrage is a staple in almost all builds but do not upgrade it because the upgrade is insignificant.
Lightning Bolt is the only Storm spell other than Energy Barrage that does not trigger the Sleep - Weakness bug and is a powerful spell if you can get enemies clustered, which you can do with Pull of the Abyss. Just stick with the upgrade that grants more damage.
Static Cage is one of the best spells in the game but it does cost quite a lot of ability points to fully unlock its potential and don't pick the alternate upgrade that does damage outside the cage because its crap.
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For Spirit, all spells are a go except for Mind Blast. Mind Blast is a close range, close quarters spell and the Rift Mage is a distance caster.
Dispel is a must have on at least one of the mages if you have the Trials toggled on. Both upgrades are good.
Barrier is, like Energy Barrage, a staple. I would encourage you to pick the upgrade that makes the Barrier stays on longer before decaying instead of cooldown reduction.
Revival is as its name implies. You should have it one a support mage and note that the alternate upgrade for Revival turns it into something like Simulacrum.
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For Focus, do not use Firestorm because it is bugged. Stick with Rift abilities that your Inquisitor gets. Both the Mark and Aegis are good. The Mark is offensive and Aegis is mainly for defense.
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Hope you have a good time with Rift Mage ! 