I have quite a lot of experience with Rift Magic so I will break it down the best I can for you.
Lorewise, the Rift Mage is a mage that uses the Fade directly as opposed to twisting and manipulating bits of the Fade. Cole explains this in great detail if you choose to be a Rift Mage.
His first comment about you as a Rift Mage:- "It shines on you, shimmering and sharp. You made magic from the Rifts."
When you inquire him on how being a Rift Mage has changed you:- "The Fade sticks to mages. Little figments, flitting, floating free, then forced into shapes. Fire, Ice, Lightning. You use the Fade itself. You make it charged but not changed, channel enchantments.
It's strong and pure and loud. You ripple like water when the stone is dropped "
Solas's views on you as a Rift Mage:- "You seem to be drawing upon the raw substance of the Fade, likely using your Mark as a catalyst. I use similar techniques, although it took years to learn them. Why did you chose such an esoteric area of study ?"
To which you can reply to Solas:- "I hoped that studying such magic would help me better understand the Fade."
He then approves of this and says:- "While our fight affords little time for formal study, the wise can better themselves even in the midst of battle. Perhaps especially then. I hope your new studies serves you well."
So it is safe to say that Rift Magic is one of the, if not the purest form and purest expression of magic for the reason because you use the source of magic itself as opposed to relying on bits of it that is around you.
This also explains why it is very uncommon and only discovered after the Breach was created. Your Trainer (love that woman) is an example of this. The magic is so pure, so powerful that it takes someone who is specially gifted in magic and have a brilliant mind to make Rift Magic work. Those who cannot, get overwhelmed and die or lose their memories.
Additionally, this gives the Rift Mage a great roleplaying advantage. You have the Mark of the Rift and is the first mortal mage in ages to be able to physically walk the Fade without issues. Suffice to say, you as the Inquisitor are tied very intricately towards Rifts and Fade, which makes Rift Mage a natural mage specialization for the Mage Inquisitor.
Other than that, the Rift Mage's esoteric-ness and complexity will allow you to roleplay as a scholarly mage who uses knowledge as a weapon, as opposed to those brutish Knight Enchanters with their spirit blades. 
Gameplay wise, Rift Mage is all about area of effects, crowd control, debuffs, mana regeneration and combos. Think of Rift Mage as the marriage between Mass Effect's Adept class and Dragon Age 2's Force Mage specialization.
Veilstrike is a cheap spammable ability that debuffs enemy. Stonefist is spammable nuke that does good spirit damage, can put people to sleep and with its upgrade, has an area of effect debuff. Pull of the Abyss is the Fade version of Singularity that drags enemies slowly to its center. With the Rift Mage passives, you can use the enemy's debuffed status to gain mana regeneration, cause them to do less damage and make you do more damage to them.
In a recent conversation with fellow BSN-er, Selea, I have come up with a decent Rift Mage build.
Build Setup
- Rift Mage - 9 (No Firestorm, no Veilstrike upgrade, take everything else)
- Inferno - 4 (Immolate upgraded, Clean Burn, Flashpoint)
- Winter - 4 (Winter's Grasp upgraded, Mana Surge, Winter Stillness)
- Storm - 6 (Energy Barrage upgraded, Static Cage upgraded, Conductive Current, Static Charge)
- Spirit - 4 (Barrier upgraded, Peaceful Aura, Guardian Spirit)
That is a total of 27 skill points. Mana Surge, Winter Stillness, Barrier's upgrade and Guardian Spirit are all optional, they are just icing on the cake here. So that leaves you with 23 must have skill points for this build which is very achievable.
Lower Level Inquisitor Skillset
- Veilstrike
- Stonefist
- Pull of the Abyss
- Energy Barrage
- Immolate
- Winter's Grasp
- Barrier
- Mark of the Rift
High Level Inquisitor Skillset
- Stonefist
- Pull of the Abyss
- Energy Barrage
- Immolate
- Winter's Grasp
- Static Cage
- Barrier
- Mark of the Rift
There are few important things to note with this build. I do not take Firestorm and instead chose to use Mark of the Rift instead and in the later higher levels, I choose to ditch Veilstrike completely.
First, Mark of the Rift is the best focus ability in the game, bar none, except for Thousand Cuts. It works everywhere and on everything, even high dragons. Secondly, it is called "Mark of the Rift" and your Inquisitor will be a Rift Mage so there is a theme synergy. Thirdly, Mark of the Rift and all the Rift Mage abilities, are all green in color which enhances the "Mastery of the Fade" theme.
Firestorm is powerful but it does not work on targets with high fire resistance and fire immunity. It is also very erratic and irregular in its animations. Plus, Firestorm is clearly intended to be a focus for the Inferno tree but moved haphazardly to the Rift Mage tree. Firestorm if good on Solas, you have an OP Focus ability that deals with Rifts so use that.
Veilstrike is not upgraded because upgraded Stonefist and upgraded Pull of the Abyss makes Veilstrike redundant. Veilstrike can be good at the beginning when you still don't have the upgrades to Stonefist and Pull of the Abyss but later, it is no longer a must have.
Static Cage is here because with the upgrade, it is a truly devastating spell, especially when you combine it with Energy Barrage, which is, in my opinion, the best single target mage spell. You could use Chain Lightning but I find its damage to not be that impressive, especially when you compare it alongside Energy Barrage, just meh. Chain Lightning in this game reminds me of a weak Chain Overload from Mass Effect 3.
Fade Step or Frost Step is also not exactly necessary since you will be crowd controlling and debuffing everyone from afar so dodging is not much of an issue.
I also recommend getting items with enchantments that reduces spell cooldowns since Rift Mage's passives will essentially give you unlimited mana so having your spell cooldowns lowered is a good thing. What's more, get those amulets that gives you better Focus generation and unlock your Focus to tier 3 as quickly as you can.
However, Rift Mage has its weakness. For big creatures like High Dragons and Giants, Pull of the Abyss and Veilstrike do not work on them. Stonefist does. That is their only weakness, it is a rather glaring weakness though so keep that in mind.
I have not experimented enough with Necromancer to give you any solid advice. I can say that their Spirit Mark and Walking Bomb works on everything. Your followers and advisers, almost all of them, will disapprove of you becoming a Necromancer so keep that in mind if you are into that sort of thing.