Keeping it simple since everyone was new at some point.
There are only a few skills worth boosting over 6, and even then thats only if you have a very specific plan and leftover points. You may want to use the skill planner at
http://www.stoacademy.com/tools/skillplanner/ to work things out ahead of time so you don't end up with leftover points or being juuuust short somewhere. Generally speaking if its a skill you expect to use a lot, put 6 in it, if its something you might use or it resists something that will be used on you, spend 3.
Your BOFFs (Bridge OFFicers) are your power set. My first char I didn't pay much attention to them at first, to my detriment. Switch the toolbar when in space flight to version 4 (I'll let you figure out how to do it

). You WILL use up all those buttons, and find yourself wishing you had more. Also I found a good post a while back that lists all the powers and how effective they are. It isn't perfect, and you may find something you love that the writer hates, but its a good yardstick when you're feeling things out.
http://forums.startrekonline.com/sho...d.php?t=254545
Don't ever buy in-game gear with dilithium unless you absolutely have to. Use the Exchange first, you'll generally pay half as much and only pay EC which are easy enough to come by. If you aren't sure and want to try something out, by the White/Common version, if you don't like it, you can toss it back on the Exchange as it won't be bound. Do the Investigate Officer Reports and Explore Strange New Worlds daily missions (in your journal) to start building up your dilithium supply for later.
Whatever kind of beam/cannon you equip your ship with (phaser, disruptor, etc), stick with a single flavor, as the damage-boosting consoles are most effective when you use several of the same kind. People will also give you a hard time if you're a Rainbow Cruiser (beams) or Skittle Boat (cannons). Sticking with one kind of energy and one kind of kinetic damage will be more damage efficient and save you some grief.
And really its your first character and you level quite quickly, so you may just wanna experiment with your first try, then delete and make a second character that you really commit to. My main is actually character #3, but with how quickly you level in this game it cost me all of two weeks.
G'luck!