I edited your post for clarity.
You can probably start doing Operations in Battlemaster gear, if you can find a group that's willing to carry you. Start picking up blackhole comms, as they allow for effective min-maxing with current BiS mods and armoring. Picking up the storymode operations and the daily HM flashpoint through the LFG finder is profitable and nets you 45 BH comms a week, if you're diligent.
You'll want to switch into PvE gear eventually, but for a while the Battlemaster is going to be best. Consider whether the PvE or PvP set bonuses are more useful to your playstyle.
PvPers tend to make excellent PvEers. Best of luck.
Holy crap, a helpful post without the snarky attitude.