PvE could be solo overland, dungeons, trials, vMA ... PvP could be raid, small group, battleground, dueling.
PVE. I might delve into PVP on rare occasions but PVE is my main focus.
This character is hopefully going to be built for a lot of group dungeon work so I can go through them often and not have to wait as long as I would with a DPS to get in via the PUG.