Power for

The dog companion is widely regarded as the best first-companion choice regardless of your class simply because it does the most damage. The cleric (healer) companion heals so seldomly and for so little that it really isn't worth it unless you are playing a Guardian Fighter who is already fairly competent with the block so that the small heals she ends up casting are just topping you off since you are always fairly high.

The dog does a decent burst damage attack and has a knock down that he uses somewhat intelligently.

Of course, this is all based on the first 20 levels or so. Once you max out the cleric companion for instance, she is healing pretty well as she has her HOT as well as her standard heal. Naturally all of the starter options are going to be worthless once they hit companion level 15 (this will probably take a good 20-30 levels for you because its easy to forget to send them to train). That is until they add the companion training books that allow you to raise their caps.

This may end up somewhat long, but here goes!

First of all, what exactly are Action Points?

(I just took the time to add this to the official wiki :D @ wiki )

Action Points are the method by which a character's Daily Powers are recharged. Each character has a gauge represented by a D20 in the middle of their Combat Action Bar. This gauge refills as the character gains more Action Points. When this bar is filled by the attainment of Action Points, a character's Daily Power is available for use. The use of a character's daily power depletes this gauge and a character must once again perform actions which grant Action Points to refill it. Each Class has a different set of things that cause the character to gain Action Points.

What abilities gain Action Points?

Great Weapons Fighter :

Encounters:

Battle Fury - Increases your Atwill and Encounter damage as well as Action Point gain for brief period. In addition, when first activated your Stamina is refilled. This power may be activated while moving.

Indomitable Battle Strike - Savagely strike your target to shows your other foes the fate that awaits them. After killing a target with this strike, you gain bonus Action Point, and nearby enemies are briefly Marked. Marked targets take additonal physical damage until they attack you.

Feats:

Unstoppable Action - You gain 5/10/15/20/25% bonus Action Points for dealing damage while you are Unstoppable.

Guardian Fighter :

Encounters:

Into The Fray - A fierce battle cry that temporarily increases your adventuring party;s deflect chance, Run Speed, and Action Point generation.

Ability Score Bonus:

Constitution - +1% Action Point Gain

Feats:

Action Surge - Gain 2/4/6/8/10% more Action Point for damage reduced by your damage reduction.

Improved Vigor - When less than 50% health, gain 2/4/6/8/10% more Action Points.

Martial Mastery - Taking damage while not using Guard now builds Action Points. You gain a bonus to this value based on your Damage Resistance.

Trickster Rogue

Encounters:

Bait and Switch - Jump backwards, dropping a decoy in your place. Any enemies that are near the decoy will attack it instead of you. Gain Action Points when the decoy is hit by an enemy.

Feats:

Action Advantage - 2/4/6/8/10% bonus Action Points for dealing Combat Advantage Damage.

Cunning Stalker - While Stealthed, you build 4/8/12/1/20% more Action Point.

Action Rush - Your encounter Powers have a 15% chance to grant 3/6/9/12/15% of your Action Point.

Thrill of the Kill - When you land a killing blow, gain .2/.4/./.8/1% of your Action Point.

Control Wizard

Ability Score Bonus

Wisdom - +1% Action Point Gain

Feats:

Controlling Action - Gain an additional .2/.4/.6/.8/1% of your max Action Point when you cast a control power.

Critical Power - When you land a critical hit you gain 1/2/3/4/5% of your total Action Point. (10 second cooldown)

Devoted Cleric

Encounters:

Prophecy of Doom - Target has lowered Defense for a medium duration, and if target is still alive after this time, They take a large amount of damage. If target is killed during this time, you gain a large amount of Action Points, and this power instantly recharges.

Feats:

Healing Action - Gain 1/2/3% more Action Point whenever you use a Healing ability.

Ability Score Bonus:

Charisma - +1% Action Points Gain

Class Feature:

Holy Fervor - Your attacks generate 5% more Action Points. Rank 2: +5%. Rank 3: +5%

Also, if you mouse over your AP meter while it's not full, it will tell you what fills it. Another cool thing to note, is that the Recovery mod raises AP gain by a percentage. For example, 2,982 Recovery is +49.3% AP gain.