The way the roulettes work now is you have to clear every dungeon/instance in the roulette once before it unlocks. Then you can roulette them, which I think is to help cases where people were specifically not unlocking certain dungeon (Pharos Sirius) so they didn't have it in their rotation. Also it does give you certainty that the people you've run it has cleared it already.

What tribe quests you do is up to you. They all are the same amount of work, but have different quests you have to do. So if you want to focus one over the others then picking one that you want their items probably is the best way to go about it.