Yeah, the stock frigate should be fine.
When you exit to the big map (Called Battle Channel), click on the big yellow plus in a circle near the top of your screen. Another smaller map will appear. Go to the "Battle Area" which is Area 12 (just above the London Harbour).
There you will see either Purple (great battle) or Green (blitzkrieg) rooms and just click to join. Those are the ones giving exp.