All right, so I've fiddled around with a few classes now. The Dark Templar is indeed pretty good for soloing, and I have one that just hit level 40. The problem with DTs is that while they have great survivability, they're not as interesting to play as other classes can be. Still not bad, just not stellar.
When Deus and I are playing together, he plays a Tempest of Set and I play a Conqueror. This combination has thus far worked extremely well, with the Conqueror to tank and DPS while the ToS does the healing and, um, more DPS. Truthfully we kill most mobs before we even have a chance to make full use of our abilities, but I suspect this will change as we level up.
Not crazy about the Barbarian. It's okay I guess, but it isn't that different from the soldier classes except that it dies more often.
I recently rolled a Herald of Xotli because I was getting sick of my Dark Templar, and man, is this class fun! Sure, you die all the time (at least at level 12), but it's a firebreathing mage with a big sword. Super fun to watch a HoX set everything alight and then finish them off with a nice two-handed combo. This class also has the best fatalities of the ones I've played so far; I'm looking forward to getting the "I eat your heart!" combo.
I doubt I'll stay interested in Age of Conan long enough to reach the endgame content, but for the moment I'm having a lot of fun with it.