Energy Levels are important in space combat. If you wonder why you don't get through an enemies shields, check if you're running at full weapon power! (Currently, weapon power is pretty much the most useful to set high.)
Skills can be hard to get at first, you will not know how things work together and effect each other. Don't waste any respecs (you get them everytime you increase rank) before you know what you are doing. You can go through most of PvE (Player vs Enemy) and probably even low level PvP (Player vs Player) with "suboptimal" builds, but later you will certainly want to find the right choice of skills.
Advancement is slow at lower levels and gets faster. The rationale seems to be that one or two missions should be enough to allow you to advance one skill, and skills cost more at higher levels.
To attain a new rank (Lt. to Lt.Cmdr), it is not enough just have the Captain skill points, you must actually spend them. If you get a new rank, you will get a new mission to return to Earth Space Dock or Q'onos.
Your Bridge Officer Powers become more and more important over time. At lower levels, you don't have much bridge officer skill points to spend for them, so choose wisely. At higher levels, it doesn't matter. Be aware that rank III abilities are rare finds on Bridge Officers. You can retrain their skills, but you probably should never retrain these. Hold them in reserve.
You need to be Lieutenant 5 (or 6) on your federation character before you can create a Klingon Captain. You get a new character slot with that (for a total of 3.)
Exploration Missions and PvP are a way to get some decent equipment. If you get to a new rank (e.g. from Lt. to Lt.Cmdr), you might first want to do some exploration or PvP and earn those badges. (PvP badges can be turned in on Deep Space K-7 or Ganalda Station (KDF), Exploration on Earth Space Dock or Q'uonos). This can also give you some skill points and experience that makes the storyline missions easier. Now, if they are too easy for you, don't do that.
PvP is hard and _very_ team focused, while the rest of the game allows a very "casual" attitude with a lot of solo play and only optional teaming. But in PvP if you don't work together and share what powers you have with your friends, or focus fire, you will probably lose. Start early if you're interested in it, and if not - there is other stuff to do and never feel forced to do something you don't like just because Cryptic is dangling rewards in front of you.