Wait for a Q-Boost weekend, and buy a C-store XP bonus to go along with it. other than that I suggest doing the Red Alerts, Exploration, and once you reach Lt. 6 (I think) you can do the Romulan Episode series (first one will be 'The Vault" from Admiral T'nae). Other than that leveling goes by incredibly fast already once you get out of the Miranda.
Oh right, don't forget to level up in an Escort for maximum speed leveling.
Use Rapidfire, High Yield when possible. Two copies if you want. Put a Tractor Beam in your ensign Sci to maximise your attack on the NPCs.
I would carry a BO with Tractor Beam 1, Science Team 2 specifically for the Breen dailies to quickly deal with the Subnucs from the Chel Grett Cruisers. That way you don't have to get behind them to avoid the Subnucs and can just blast them away from the front after tractor beaming them.
Don't forget to put your power levels at 100/25/50/25 in your escort.
Oh right, I forget that Scatter Volley is great for those clusters of NPC ships and Torp Spread is OP right now, so that would be better than using High Yield for NPCs now.
I never have issues dispatching them with RF or HY, but it's up to you.
Don't forget about the Sh'mar daily near that Starbase southwest of Drozana.