Fastest way is exp in Deep Space Encounters (switching between instances during cooldowns) and then going to Exploration zones to exp when DSEs are in cooldown.
But I wouldn't advice rushing through the content if you're nor an Admiral yet, because you're going to run hard into a brick wall of bordom when you run out of stuff to do or repeating the same missions over and over for the sake of gear or accolades.
Pretty much the only thing I can do at RA2-RA4 at present is diplo missions and cluster exploration missions. They don't seem to have any episode releases for those levels, I've checked every time I've leveled and no new missions save for a random diplo mission on occasion. So I can only assume it will be the same until I finally hit VA.
Of course once they start releasing weekly episodic content that might change, but knowing how it goes, those will be VA exclusive. *sigh*
I'm RA,UH4 and I haven't had a new mission in at least 2-3 levels save for previous missions like Terrordome and Khitomer Accords which I don't do simply because I've heard how horribly bugged they are. I would love to do a run with those, but then again can't find a group to stick out a full mission segment. Darn shame.
Hi OP: I'd recommend hanging out in the Gamma Orionus Borg Sector missions. They give 500+ Skill points per completion (that's nearly half a level for doing one mission - good stuff). There is a small cooldown on accepting the mission again, but it's not too long. Do those for 2-3 levels from your present RA level. At about lvl 47, the sector missions will only give you about 300+ skill points which means it's time to move on.
Next do your episode missions in succession. Those give 500+ skill points and should take you to at least lvl 49/50. From 49/50 head over to b-train, the Vice admiral section and do the dailies/explorations. You should be vice admiral in no time.
This method worked well for me across 2 RAs. Congrats in on VA in advance.