I recenty made up a new fed engineer and RP'd him like he was a true explorer and just patroled all the planets in the game and I got to level 50 before I finished the Alpha centauri sector. My course started in the Sirius Sector, moved to Regulus, then to Eta Eridani and then to Pi Canis. I also did a few explore missions in Delta Volanis and the Hromi cluster and did some Dilithium grinding. All this without doing and mission past the Azura mission(basically I thought I couldn't live without the comm to the Azura II).
Also have to add that Doff'n also levels you up A LOT! and it was really fun and made the game seem like it had a behind the curtain feel to it.
Q: [quoting Hartley] "Nothing reveals Humanity so well as the games it plays..."
The first thing I've did is the trainer mission (the first mission where your ship was attacked by Borg) to boost the lore rpg! When I become a Official Lieutenant, I do only the SS Azura rescue mission. Later I don't play the story line mission, but I will run only exploration missions, patrol and after level 7 I will start with Doff assgn.
I hope that this way to leveling isn't hard to reach lvl 50, but I'm very bored to redoing the story line mission (for the third time).
It would be slow, but no two pvp matches are ever the same, and it will build up slowly your experience in the game, so that if you ever decide to try VA pvp you will have more solid grounding than people jumping in after only pve'ing.
Ker'rat used to be pretty good for leveling, but haven't done that in a while(just starting second Fed toon). Leveling via only DOff'ing takes quite a while, but only requires a few minutes of your time each session. Most daily missions aren't too hard, and most reward dilithium along with the Exp you get, so hitting those can be a good choice.
The last toon I brought up KDF side, I mostly did Empire Defense daily missions and DOff'ing, only bothering to do a few missions with good gear rewards. Did that up until hitting 44/45, gaining the ability to do proper STFs. Note: STFs give surprisingly little Exp, DOff'ing and Red Alerts is most of what leveled me from 44 up to 50.