OP, you are looking for campaign-long antagonists. So, the question is, what are you in the mood for? Think long-term, since the campaign is going to focus on them. What are you looking for? What ever you do with them, it's going to last a while, so use something that won't get old fast.
Orcs typically mean a War campaign. Because they breed fast, they're physically strong and aggressive, and they typically rape and pillage.
Traditionally, Orcs have been ye olde irredeemable evil monster. They're the thing you slay without question because you know even if you took one, dressed it, bathed it, and sent it to school, it'd beat the classroom to death with its chair.
If you don't want them to be just irredeemable monsters that just destroy and slay (because a campaign focusing on them would get old, fast if they aren't Interesting), then there are some other options:
1) Accentuate the Chaotic over the Evil
Orcs are not evil, per se, but they are a race designed for one fuction: toppling things over before they get too dangerous, bloated, or otherwise advanced. If decadent society, Knowledge Man Was Not Meant to Know, or Technology Too Advanced For Their Own Good was a Disease, then orcs are the disinfectant. Every so many (insert time here), orcs sweep across the land, tearing cities apart and burning the libraries to the ground, and the world restarts again. Too much Order, and the cycle starts over.
Or, for a less epic relevance, orcs are the reverse of humans. Where humans seek to spread, to master, to conquer and control, orcs seek to take, indulge, revel and forget. An orc is passionate, short sighted and easily given to impulse. Their inevitable nature gets the best of things like loyalty, discipline or order. They are instinctive agents of chaos and anarchy; the only thing you can rely on an orc to do is not be reliable, unless you simply make him do it (hence, how orcs get anything done as a group). Add in a propensity for aggression, with no patience for diplomacy, and dealings with orcs falls into passifying their whims, forcing them to submit, or taking up arms. And the only thing an orc knows how to do better than revel is hold a grudge. (So Orcs: big, strong toddlers).
2) Go with Historical Precidence
Model them after an existing historical culture. Not ye olde tribal (Native American/African/Klingon) but something a little more destructive:
Norse Vikings (Think about it, Gruumsh and Odin have some really strong similarities). You have your "rape pillage and plunder" orcs, backed up by gods of Strength and Thunder, all seeking to sweep their reach long and hard, and die a grizzly, bloody death so their Gods can give them the eternal high five. Orcs that do not make it to Orc Valhalla are reincarnated as non-orcs. This is one reason why Orcs are so ok with slaughter; they are liberating the souls of former orcs, so they can be reborn and a have glorious death!
Mongols (horse riding, spear throwing and barbed net using raiders) or Hun-style large beast-riding (rhino, elephant, etc) warbands united under one banner. Part of why they dismantle civilization so it looks like Mongolia under Khan, rather than just a smoking crater (or what happened to Europe after the Huns).
Spartans or Persians. No, seriously. Spice them up a little 300 style as either group. Exotic fighting styles, raiders from the far off land seeking to plunder for their Godking. Or a race bred for war, bred to fight.