What is the best specilization for each class?

It really depends on your play style for the different classes. I've only played mages and rogues, so I can only talk about my experience with those classes and specializations.

For rogues, I've only played archers. When I go with the Tempest specialization, I usually skill Leaping Shot, Throwing Blades, Hook and Tackle, the Electricity Flask, the Fire Flask and the Cold Flask as my six main skills. That way you can combine for example the Fire Flask with the Throwing Blades and deal a lot of damage with that. Or the Leaping Shot with the Electricity Flask. I usually put the Hidden Blades masterwork fabric on my bow, since it procs relatively often and combined with the Cold Flask deals a lot of damage as well. Tempest is the specialization I use for an archer who gets up close and personal every now and then.

Assassin is also nice, but I haven't played it as often. I went with Stealth, Long Shot, Hidden Blades and Mark of Death as my four main skills there. Deals a lot of damage over distance and a bit distanced from the fighting itself. I haven't played the Artificer specialization myself yet, but I've used the bombs with the Hunter in multiplayer and it's also a lot of fun. Plus, reduced cooldowns with one of the passives.

For mages, the Knight-Enchanter works best for me personally with a mage who really is in the middle of the fight and deals a lot of damage. I skilled for fire damage and only produced the barrier through the passive and used the Fade Cloak as well. Though I mostly use this specialization for the passives.

Rift Mage is nice if you like crowd control, since a lot of the skills itself are great for that, plus you get the combo of Chain Lightning and Stone Fist. Also great specialization for a mage who really is a ranged character.

With mages? The last mage I played and enjoyed the most was a glass cannon. I had the Superb Belt of the Inferno Pact and the Lyrium Sigil and was running around with 140HP towards the end I think. I was also wearing the amulet that increases the critical hit chance for every non-critical hit and had a lot of heal on kill and critical chance and damage on my staff. So with that mage I was mainly focused on damage both to kill the enemies, but also to keep my barrier up due to the Knight-Enchanter specialization. I mostly used Immolate and the Fire Runes, with all the passives from the fire tree. But I also had the Spirit Blade, Fade Cloak and Chain Lightning for enemies with resistances. And I was always in the middle of the enemies so the runes dealt the most damage.

I also always had another mage with me that I skilled for support and crowd control, so I could get another barrier or get revived if I died, which happened a lot towards the beginning and still a bunch towards the end, since I was pretty much a one-hit-wonder.

Do you have Trespasser installed? Everyone used to say KE was best, but it got nerfed. Now, as of Trespasser, Necromancer is best of the mage specs.

It kind of makes sense that you struggle with KE if you also have trouble with rogue specs. KE can be run as a melee combat character, so if you're not comfortable being toe-to-toe with a mob, KE isn't for you. Although, there is a variation of KE that uses all of Winter and does not use Spirit Blade, which is a purely ranged attacking mage with a lot of durability. Infinite barrier regen with Ice Armor on top is pretty invincible. You'll never have to worry about being backstabbed by a Spy.

You'll like Rift Mage. It's one of the easiest specs to play. Just spam the hell out of all of the actives: Stonefist, Veilstrike and Pull of the Abyss.

Once you get the hang of it, you'll start so see some obvious strategies. For example, Pull of the Abyss pulls a mob towards a single point. So, why not lay down a Searing Glyph fire mine first, which takes time to activate anyway, and then put a PotA right down square in the middle of it? Pull all those mooks towards the mine so they can be blown sky high! Such fun.

At the very start of a battle, Veilstrike the enemy ranged attackers and then sic your melee characters on them while they are flat on their backs. If you time it right, those enemies die before they even get a chance to fight back.

"Best" is very subjective. It is simpler just to mention personal favorites. As far as personal favorites are concerned, mine are:

Rogue: Artificer by far
Mage: Rift Mage, by a small margin over the other two
Warrior: I don't really like any, but I would vote on Templar for roleplaying purposes.

There's not so much a "best" so much as "the one that most compliments your playstyle".

Try playing some of your companions that have certain specializations so you can get a feel for them. Let your Inquisitor rack up skill points as you try to find which one you prefer.