Matewis: Probably there are a few terran/protoss levels mixed into the campaign, just like there are about 4 protoss levels mixed into WoL's campaign.
But yes, I'm not a huge Zerg fan either, though I like them more than the Protoss. It really bugs me in an RTS when I have units that can't be healed in any way. Which was a nice tactic to use with the Zerg when playing against protoss. Using the [url=http://starcraft.wikia.com/wiki/Defiler_(StarCraft)]defiler's[/url] plague ability you can, in effect, permanently halve any protoss unit/structure's health. Ie full shields but only 1 hp.
But overall this is one reason I like Warcraft more. I love playing each of the 4 factions.
Yes, Defiler was pretty mean with its plague ability...just imagine if someone does that against a group of super-expensive carriers :-) (even more extreme would be a 2vs2 with a Terran ally who would use the science vessel's EMP wave...in theory you could reduce Protoss units to 1 HP just by those special abilities). Though when I played multiplayer, it rarely got to that stage.
I can't really recall if HotS had any missions where you control Terran or Protoss units (though Raynor's raiders do play a part in the story iirc). LotV has a set of three missions right at the end where you control Protoss, Terrans and Zerg respectively.
Breja: Protoss were my favourites, and I always regretted their campaigns came last. Though, to be fair, I liked them so much not for gamplay reasons (I never really learned to play them well), but just because they seemed the coolest and most unique and interesting to me.
Matewis: They were last in the original I think, but first In brood war if memory serves. Gameplay wise, even apart from the no-healing aspect, I wasn't nuts about the Protoss. I seem to recall finding Protoss missions the most difficult overall. But I think also I was just horrible at playing them. Things did start to get easier once you managed to get a few carriers out, and some of those giant worm artillery things.
But anyway, Terran all the way for me. I always like the badass human faction the most. Humans in Warcraft 3, and Space Marines in Dawn of War.
I liked the Protoss a lot, their expensive but powerful units appealed to me, and there was a tragic sense of a doomed civilization, threatened by extermination and riven by fratricidal strife, in their story in SC/Brood war that was really great (unfortunately that was mostly lost in LotV which is just dreadfully boring).
Terrans always seemed to be the most difficult race to me because they've always involved a lot of micromanagement. They did have some really cool abilities though that could be devastating in the hands of a skilled player (like siege tank drops on cliffs in that Lost Temple map...or the science vessel and its irradiate ability).