Some hotkeys: These are available on the top right portion of the UI, the one with the minimap. However, its hard to find them sometimes.
press K to bring up your skills menu. this shows you all the places you've invested skill points (SP) in. you will be limited to the first set of skills until you get promoted.* Use the ^ arrow to increase a skill, then select "accept" at the bottom right of the window
you can also see what your bridge officers' (BO) skills are. you acquire bridge officers at set levels. each bridge officer can learn up to four skills, gaining one each time you promote them.** for space combat, all Bridge officers are about equal.
if you don't know what to do, press "J" to bring up your missions. this will only show the missions you have accepted. go to "Available" at the top to see missions you can accept.
to go places, it is easier to use the map "M." You can go to "area map" to see your surroundings, and you can click on a planet to set a course for it.
Galaxy map will show you the different sectors and how to get from one to the other. System list shows you what the area map does; only in list form.
I will say there's no real point in ramping up the difficulty until you reach the max level. Difficulty only increases your chances of getting rare loot. You can usually get rewards from missions that are equal to the best loot at that level. Plus, it takes much, Much longer to do a mission on elite difficulty.
Honestly, you should have no problem with anything but elite difficulty or the endgame raids no matter where you spend your points.
*to be promoted, you need to spend a certain amount of skill points. it is equivalent to the number you need to reach level 11. for later levels, it will be equivalent to 21, 31, 41, ect.
** you promote bridge officers when you are promoted. hit "K", go to status at the top and your bridge officer's name at the right. at the bottom-center of your BO's status screen is a button that says "career options" click it, select promote. You will need to have spent a certain number of Bridge officer points to promote.
I apologize if I am repeating anything other people said, I was crushed by a wall of text.