With my current character, I am trying to do a build that is straight dunmerian. I've joined the Tribunal Temple, and will probably join the Morag Tong, and i don't want to join ALL the factions because that seems silly RP-wise, but I am unsure as to which Great House I should join.

Do the Great Houses serve as good alternatives for their Fighter/Mage/Thief counterpart guilds? At least, it seems to me that's how they are set up, what with the skill required for advacement and such. I was originally thinking Telvanni, but now I'm no so sure. My character has skills spread over stealth, combat, and magic.

Not looking for major spoilers or anything, just some suggestions.

Yes they do.
As you've noticed, each House is based upon one of the three styles of gameplay. Combat/Magic/Stealth
Since Combat is usually the easiest to level, your character might want to join House Redoran.
Redoran also has close ties to the Temple, so it makes sense from a roleplaying aspect, too.

Check the Favored Skill/Attributes of each House on the wiki before you commit to a House.