It does sound like you are quite new to the whole 'Powers' thing, so to that I would also like to say that even though by now you may have looked at the galactic powers tab, there is a lot to take in from there, so to help a bit...
the first choice often made is to Federation or Empire or Alliance or Independent due to what that name might imply to a person, I originally chose Federation as I am a Trek fan, big mistake this federation is nothing like the trek federation..
The overall take for each Power is a very simple decision and often ends up not as expected.
The next 2 things are more often the real deciding factors, putting universal political and religious beliefs aside, and those are what benefit does each group for each power offer, in there you will see bonus payouts for cartographic data sales, bonus payouts for bounties.
Then the main things that drive most people at one point or another in the game is the physical reward for joining a power, such as prismatic shields, The Imperial Hammer Rail, the Pacifier Frag Cannon, the Packhound Missiles are a few of the popular choices which often lead to at least a temporary pledge to a member of one of the Powers.
I hope that helps...most all the info you need to be able to decide is in the Galactic Power screen