What's the most powerful lantern corp?

None of them. If you read Johns' GL then you see it is a game of rock paper scissors. Blue and Green are the most powerful if they are paired together since blue boosts green and green unlocks blues offensive abilities. Red has raw power, but no control and usually can't do anything other than spew napalm breath(is exceptions in recent years). Yellow is more powerful than all the others if it can instill fear in the other lantern corps, but when they don't they are not nearly as effective. And it goes on and on where every one has pros and cons so it largely comes down to the person wielding the ring than the ring itself.

If we don't count white/black, then probably Orange. There's only one member, but he's able to summon an entire corps of constructs.

Corps probably White or Indigo. Ring is of course is Phantom Ring.

Probably White then Orange. The official White Lantern Corps only technically appeared in one issue and hasn't since, but they would be the most powerful because they are all the colors and their powers combined. Next would probably be Orange, but again it doesn't necessarily count as a Corps because there is only one Orange Lantern and that's Larfleeze, who has all the power of the OLC in himself. Next would be Indigo Tribe, which would probably be the most powerful corps proper. There's a lot of them and they can channel any one color at a time and redirect the energy, as well as teleport anywhere in the universe and basically brainwash individuals and completely change their personality.

Its super cheaty, but excluding black and white its absolutely Orange, however that's almost entirely off a technicality since Larfleeze is the only Orange Lantern and he's his own power battery.

Barring that its absolutely Indigo.

Proably Kyle Rayner. But in terms non reality warping corps it's Proably Orange Green Yelllow Violet Blue with red and indigo at the bottom due to circumstances.

Kind of a matter of perspective.

First is the question of strength in numbers. Black Lanterns spread through death, basically like a zombie plague. There is no special training or quality of character required to be a Black Lantern, you just have to be no longer living. This ease of recruitment makes them VERY dangerous.

There's also just actual capacity to wreck shit. The Red Lanterns have the most immediate raw destructive power. Red Lantern Napalm eats through everything, including power ring constructs themselves. Combined with the berserker nature of most of their members and the blood magic Atrocitus is packing, and that's a force to be reckoned with.

The Orange Lanterns are beholden to the will of a single Ring-Bearer/Battery-Holder. It is an entire Corps following one guy, and anybody he kills gets added to his ranks. But it's also pretty unorganized, just like Larfleeze himself tends to be, and the individual constructs aren't all that strong.

Yellow Lanterns are chosen somewhat selectively, and have to go through an ordeal. While Sinestro CAN give out Yellow Rings like candy, members of the Sinestro Corps have to go through an intense tribunal of facing and mastering their own fears before they're signed off as combat-ready by the mustachioed eggplant himself. In addition, they're able to draw power by an emotion that they instill in others, and not just from themselves, which is a pretty amazing thing.

Green Lanterns lie in the middle of the spectrum, and have the most control of their rings and abilities. All you need is willpower. The Green Lantern ring is, in a lot of ways, the easiest of the rings to wield, which is pretty great in its own way. The neutrality of will, the longest-standing military and police traditions, and the training and infrastructure of the corps in general are extensive and strong. Green Lanterns take something basic and keep plugging away at it until it's a force to be reckoned with.

Blue Lanterns are like Yellow Lanterns, in that they have to go through an ordeal of sorts. Saint Walker had to face the impending doom of his people and keep hope in order to earn his ring, and candidates for the Blue Lantern Corps are chosen one-by-one by each new ring-wielder. They have incredible healing abilities that none of the other Corps can really match, and although they must be with a Green Lantern to unlock their full potential, they're basically space monks who can use their rings to boost their own hand-to-hand combat abilities on their own, giving them a simple-yet-effective fighting style. The Blue rings can also pacify the Red and Orange Lanterns.

The Indigo Tribe can copy any other color on the emotional spectrum, including Black, but the rings brainwash their members, turning them from remorseless criminals into beings that can basically only feel compassion. It has never been stated, but I would imagine that the simulated emotions that the Indigo Lanterns channel are inferior in power to actually harnessing the strength of your own emotions. This is why when Hal charged his ring off Black Hand's forehead, it was a weaker, less capable charge and his ring wasn't running at full capacity.

Star Sapphires can capture and brainwash their enemies. They are able to use the love that others feel to achieve certain goals, and are the only Lanterns I can think of besides Yellow that draw a certain power from the emotions of others. Their rings, like the Red Lanterns, are also more likely to control them, being on an extreme end of the emotional spectrum. With the full control and range of abilities that Green and Yellow Lanterns have, plus some bonus powers, they're a force to be reckoned with.

When bequeathed by the entity of life itself, the White Lantern Ring is an item of limitless potential. Or if you go Kyle Rayner's route, it involves mastery of the entire emotional spectrum, giving you full access and control of every ability of every other Lantern. Of course, it's incredibly difficult to actually pull this off, and requires a near-complete understanding of yourself to do. However, mastering every emotion doesn't necessarily mean being as powerful in any given emotion as dedicated members of one Corps. It'd be a hell of a fight, but I can see lots of Lanterns beating Kyle.

Black/White probably.

I'd say White.

You should really just read the whole Johns era of Lantern books. It's a great story, and since Geoff Johns created the different corps as they exist today, no background info is really required and you get to learn things as they begin to appear for the first time.

Basically Larfleeze is the single most powerful Lantern character since the "Orange Lantern Corps" members are all his constructs, but the corps themselves are just about equal (barring Black and White).

Think it should be corps in your questions.

I'd have to go with the Red and Black Lanterns.

Black Lanterns need to be hit extremely hard to be killed, usually with more than one light from the spectrum to be completely eradicated and their numbers are more than likely larger than any corps in existence, not only that, but their leader is probably the entity of Death.

Red Lanterns, Atrocitus alone is a force to be reckoned with. Atrocitus and his Red Lanterns can have their battery destroyed and still have power from Blood Magic, the Rage from others, and their own rage. When they first attacked, they were after Sinestro and tore through both The Sinestro and the Green Lantern Corps, and the plasma they spit from their mouths melt through shields and cause power rings to slowly lose their power.

Vice is a good example of a red lantern with no limits, after he was released from his Sciencell (don't think that's the word) he started killing every black lantern in his path, then immediately started killing everyone else. Until that stupid Alpha Lantern ruined everything.

Honorable Mention goes to the indigo Tribe, being able to channel power from any emotion in the spectrum is very useful and very powerful if they use it right. Like John Stewart.

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Blue light is the most powerful color, but they're useless unless they have a member of another corps with them