Well I can't speak for my two buddies, but we're looking for some constant pvp to keep us busy. I can't speak to ranked vs. reg, as rank didn't exist when I left swtor before. The game has changed a lot since then which is part of the reason we're coming back.
We do enjoy pve as a way to fill time, but we really enjoy pvp as fights don't always follow the same pattern because of the dynamic nature of pvp. Again, I can't speak to the type of pvp or the intensity we plan to have with it, but a healthy community trying to do it, pub or imp, is what we're looking for.
Personally, I don't feel you need to be on a pvp server to be good at, or do a lot of pvp, but I'm not sure if that is how it has worked out for swtor over the years.
I could care less about trolls as those are easily ignored. I'm more concerned about the 3 of us queuing up and getting into competitive/entertaining matches where it doesn't always feel like we're getting slammed or we're just overpowering the other team, or where we have to wait forever for a queue to pop. I understand some player comps/times of day are better for queue pops but that's to be expected.
I don't know if this experience exists in swtor anymore, but I know it did in the early days for me as a pub. It was fun then, but other things drew me from the game.
I don't know that an RP or PVE server is the spot for us, but if they have a fairly healthy rate of queues popping then that is really what we care about.
Does that help describe what we're looking for?