One of the Deferi missions give a reasonable amount of XP and can be finished rather quickly.
Repeting it over and over improves the level up considerably. Then there is the Foundry Daily which gives Marks / Emblems for Equipment.
The 8 story missions are high quality and I recomend them to play.
Otherwise there are the empire defense missions which can be repeated over and over as wel las the exploration.
The featured series will give the most XP per mission, but the Exploration zones are nice also when you do the 3 plus you can find data samples for crafting, and earn badges of exploration, which you cannot in the Featured Episodes.
But the featured episodes give some great gear for both ground and space as rewards, while none of the Nebula or Expanse missions in the heart of Klingon space do.
The Klingon 8 mission story arc does score well, I think you get the first 4 at Lt Cmder 10 and the next 4 at Cmdr 10, if I recall correctly. The Shard of Kahless Bat'lth you get from the last one is awesome!
PvP will also get high XP, but especially at lower ranks it can be difficult to get these days. If you don't mind waiting in qeue for a match, it'll still give some of the best XP.
The Breen series mission "Cold Comfort" Is a good repeatable mission. I can do it in less than 5 minutes because there is no combat at all in the mission. I always do that featured series and then do that mission. With the other Breen repeatables plus skill pionts for kills I can always get over 1000 skill points per day on just that.
The fastes way right now are the DSE-like missions in the Nebula, at least until level 6 (on any rank)..
They seem to be broken and you just have to complete them once instead of 3 times (but only those at the right rank).
From the 7th level on each rank they just give ca 200XP wich isnt enough but before its between 500 and 300 that works, especially with an ex boost.
#1 - Do all the "normal" missions (Not patrols etc.)
#2 - Buy 1 hour skillpoint bonus (or 8 hour) from exchange
#3 - Activate bonus
#4 - Hail all missions
#5 - Go do the patrols while bonus is active.
#6 - Enjoy your 7-day-built VA
do any and all story line missions as they become availible.. DO all the series missions at eah rank (the scaled gear will make life easier) Otherwise just grind exploration missions and farm crafting mats..
The badges you can either just keep for the unified badges coming some time in the far future or just by ship engines end vendor the things for cash
The little trick of not turning some missions in untill you have a bunch od em and using a XP token is a good idea but that'll only really work on weekly series missions.. some must be turned in to get the next mission unless your doing replays.. THEN you can trun 'em in all at once, If you find you need cash just take the first defari mission and keep doing it over and over and over.. the ships sensor dish can be vendored for quite a bit of e-creds.