Unsure of whether to level a DPS or a Tank first

[KageTokage]

It depends on your skill. DPS is more brainless and less mission critical. If you screw up as a tank you ruin it for everybody in the dungeon.
If you go the tank route, I recommend just watching a youtube guide of the duty you are about to go on. It'll take 5 minutes but it'll ensure a much smoother run every time. If you don't feel like making that commitment, then DPS would be your better choice.

I'm kind of disinclined to view DPS as more brainless simply on the basis that they aren't required to play well and deal DPS within the expected range for their gear level. I tend to bemoan having to do dungeon runs with low DPS more then anything else (Save for exceptionally bad tanks/healers who are letting party members die regularly) as they force you to go through additional cycles of a boss' mechanics and also put more stress on the tank/healers both for dungeon trash and bosses. I simply can't keep a tank up during big pulls if the DPS can't start thinning out the mobs before I run out of cooldowns.

A tank's personal role is also generally not much more complicated then:

1. Get aggro
2. Turn enemies away from rest of party
3. Mitigate tank busters

It's only when you get into stuff like extremes and savage that you need to worry about more then that.

[Edax]

I'm kind of disinclined to view DPS as more brainless simply on the basis that they aren't required to play well and deal DPS within the expected range for their gear level. I tend to bemoan having to do dungeon runs with low DPS more then anything else (Save for exceptionally bad tanks/healers who are letting party members die regularly) as they force you to go through additional cycles of a boss' mechanics and also put more stress on the tank/healers both for dungeon trash and bosses. I simply can't keep a tank up during big pulls if the DPS can't start thinning out the mobs before I run out of cooldowns.

A tank's personal role is also generally not much more complicated then:

1. Get aggro
2. Turn enemies away from rest of party
3. Mitigate tank busters

It's only when you get into stuff like extremes and savage that you need to worry about more then that.

I agree and disagree. I could be tanking for a pug and yeah it sucks if the DPS is very low or they keep dying repeatedly during a boss fight, but it's not mission critical. A tank and healer could defeat a boss on their own. If I'm a DPS and the tank keeps dropping dead, then we've hit a dead end in the run, I gotta eat a penalty to just leave.