I'm hoping flashpoints first and foremost, if you are asking this to judge priority. After that, Heroics, and then Operations.
Operations are usually handled by guilds or groups of friends anyway. Heroics can usually be done by gathering a few people on the planet, if not soloed pretty easily.
When WoW did their "raid finder," they had to add an additional lower level of difficulty. So rather than their raids being easy (which they most certainly were) the raid finder difficulty was "Click here for epics."
Don't do that.
I'd be fine with everything but operations. Flashpoints and Heroic Missions are definitely the most important. Granted, accessibility is huge in MMOs now. Clicking a button and being able to raid is a HUGE advantage "that other game" has. Bioware will eventually need that to compete.
And with how spread out the population is, the only option for the group finder is for it to be cross-server, or queues will be too long. I know it's going to be single server at first, but it's guaranteed that this tool will need to be expanded to cross-server. Just watch. I expect a lot of hate for that comment, but I'm just being realistic here.