It's hard to answer your question, because it would be very easy to spoil something for you.
Since you haven't played Origins or DA2, but have been playing around with the Keep, I'll assume you know the gist of it.
From a raw story perspective, mages have a more direct involvement, since one of the beginning plotlines is the "Mage-Templar" conflict.
From what you're asking gameplay-wise, each class has what you ask, but in different ways.
Here's a rundown, with some "Ideal Abilities" from the core class, not saying that you MUST take them, but they are abilities that I find myself always choosing, so I present them as simple suggestions.
MAGE
(my personal favorite, so I admit my bias)
Damage - it's all elemental, which bypasses armor (so armor-penetration on a staff is useless), so while it's not MAXIMUM DPS!!!! it is very reliable and consistent.
Every time you complete a basic attack combo there is a secondary effect based on the element of your staff.
(Fire=Burning=DOT, Electricity=Shocked=magic resistance reduced, Ice=Chilled=movement and attack speed reduced)
Your damage-dealing abilities are effective because you have the greatest AOE of the three classes, and most of your abilities have secondary effects which deal additional damage, make it easier to deal more damage, or make it easier to make more attacks. A triple-win.
Defense - easy access to Barrier spell (obtainable at first level-up) and Guardian Spirit, a passive that gives you a full barrier when your health would normally be reduced to zero. It has a 60 second cooldown, so it is not overpowered. If your health is going to zero more than once every minute, something is very wrong.
The only downside to Barrier is that it decays over time, but the upside is that it's an "all-in" technique, you use it and get a full barrier every time.
Fade Step is easy to acquire too, useful to position yourself or get out of a tight spot VERY quickly; can be upgraded to deal decent damage and inflict Chilled.
If you really want to buff your mage's defenses, then the Knight Enchanter specialization is for you.
It's my personal favorite, but it has passives that increase you maximum barrier, slow down barrier decay, deal damage to enemies that attack you, AND enables you to generate barrier every time you deal damage. The more you're surrounded the more powerful you get, the more damage you take the more is returned, and the more damage you deal the tougher you get.
Rift Mage is all about weakening enemies while dealing lots of Spirit damage (Spirit damage partially bypasses all defenses). Lots of offense and throwing bad guys like ragdolls for excellent crowd control.
Necromancer renders enemies Panicked, with lots of abilities that raise fallen enemies to fight for you. The more death you make the stronger you get.
IDEAL ABILITIES = Barrier, Energy Barrage, Chain Lightning, Fade Step
WARRIOR
(my second favorite, Weapon and Shield preferred, bias noted)
Damage - Two-Handed (T-H) has a wider arc than Weapon-and-Shield (W-n-S), so hitting multiple foes at once is common. W-n-S is more mobile, with Lunge and Slash being self-explanatory, and Shield Bash can be upgraded to rush forward. Abilities like Charging Bull enable you to knock enemies down, basically free hits, and others like Combat Roll can be upgraded to deal damage.
Defense - obviously, W-n-S is more defensive, what with the shield and all. Warriors are also the only class able to generate guard with their abilities. Guard is effectively a second health bar that must be depleted before health takes damage. Unlike Barrier, it does not decay, but it generally has to be "built", i.e. there are very few ways to get full guard all at once. The best part is that guard generation is not restricted to weapon type, all the main guard generating abilities are shared among the weapon styles.
If you really want to bolster your defenses, then Champion is for you, they are the only specialization that has abilities that give you full guard instantly and several passives that boost your armor and maximum guard. Reaver is all about damage, but it's risky, since the damage bonuses increase the closer you are to zero health. Templar is my favorite, and is generally a support role, with passives that increase damage to demons for the whole party (very useful, since there are many Fade Rifts [explained in-game, no worries] and they all spawn demons) and give the whole party a universal increase to elemental resistances (Fire, Electricity, Ice, and Spirit).
IDEAL ABILITIES = Charging Bull, Combat Roll
ROGUE
(not my favorite, so this will be comparatively sparse)
Damage - highest single-target damage, many passives add effects like bleed and poison. Dual Daggers are VERY fast, and daggers have the highest DPS of all the weapons. Bows are faster than Staffs, the other ranged weapon. A lot of your damage is situational, via flanking, stealth, and timing. Stealth is your bread-n-butter here, it serves as offense, defense, and utility. It reduces your aggro and gives your next attack a damage boost. Several abilities help you to set up attacks just the way you want them, like Full Draw deals bonus damage if your target hasn't been hit yet, and Longshot deals bonus damage if you're really far away from your target.
Defense - they say the best defense is a good offense, and the Rogue embodies this concept. That said, the Rogue does have some abilities to take the edge off, namely Stealth, but others like Caltrops fill the surrounding area with spikes, dealing damage to anyone who steps on them while slowing their movement.
Hook and Tackle lets you zoom across the battlefield by latching onto an enemy and pulling yourself to them, handy for escaping a difficult foe and taking out a mook all at once.
For specializations, Assassin is all about dealing insane damage in very short amounts of time. Abilities like Mark of Death deal instant, unblockable damage that you can trigger whenever you like.
Artificer takes the trap-making aspect and runs with it, allowing things like Fallback Plan, essentially a "Get out of death free" card, and Elemental Mines, which is Caltrops on steroids.
Tempest, my personal favorite, involves flasks of fire (abilities have no cooldown and knocks back enemies that attack you), ice (increases armor and damage resistance and freezes enemies that attack you), and lightning (you move incredibly fast, i.e. everyone else slows down)
IDEAL ABILITIES = Stealth, Hook and Tackle
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Yes, that's a lot, so here's a summary:
Mage = AOE, Barrier, elemental damage
- Knight Enchanter = Barrier, nigh invulnerability
- Rift Mage = DPS, AOE, CC
- Necromancer = Panicked, extra "allies" in combat
Warrior = Guard, Aggro
- Templar = damage resist, demon-slaying, no-sell on enemy magic
- Champion = Guard, Guard, Guard
- Reaver = health steal, low health means more damage
Rogue = DPS, Stealth, flanking attacks
- Tempest = ability spam, knockback, rapid-fire, extra potions/grenades
- Artificer = traps, mines, a "Plan B" if it all goes south
- Assassin = raw damage, insane DPS
Granted, this isn't everything, so pick the one that looks the coolest to you.
Each class has offense, defense, and utility, just in different ways.
And if you REALLY can't decide, just pick Mage, since mages have a bit more involvement with the story.
If you don't like it, you can bring a party member of a different class and play as them.
9 total companions if you recruit them all, and each one gets one of the specializations after a certain point, so you can experiment and see which one(s) you like.
Hope this helps, and Merry Christmas!
NOTE: Thanks to a suggestion by PapaCharlie9, I'm going to copy this into a new thread I'm making called:
"Beginner's Guide to Choosing a Class in Dragon Age: Inquisition"