The best advice I can give you is to take it slow and try to enjoy things. Everyone always rushes through the Missions without reading the text or taking time to really explore them. The overall story can be quite compelling if you take the time to read it. Also, many of the Missions have hidden Accolades in them which you can only find by taking the few extra minutes to look around the various areas to find them.
Also, don't worry about trying out new things. A lot of people worry about doing something that could ruin their character down the road, like taking the wrong bridge officer or giving them the wrong skill, but the game is really very forgiving, and even without the 'best' build, you can do just fine in most things. (Exceptions: PVP, and the Special Task Force Missions you can do when you're an Admiral)
For ships, when you can get new ships, just pick whatever you think you would have the most fun with. Don't worry about picking the 'wrong one' for your class or anything (any combination works). If you're a free player, the only thing you might want to be careful of is how you manage your captain's skill points, as free players don't get free respecs, and must buy them from the C-Store. There, I would advise reading what the skills do, and just put skills up to 6 points unless you're absolutely positive you want every last bit of benefit out of a skill.