The choice of a race is the most important decision you'll make when you start a game. There are over a dozen races to choose from in most games. There is no one race that is BEST . . . if there were, we'd nerf it to bring it into balance again. But all the races are different.
You can see short descriptions of all the races here.
You can see a list of all the races here, with links to more detailed descriptions of each race.
Each race has different strengths, weaknesses, and opportunities. Try them all and see which one you like best. The strategy for winning with each race is different. You will have (for instance) a very different experience as a Cosmic Needle Man than if you start as an Orn.
Here are some of the things you should look at for each race:
Starting population, and the EI of the homeworld . . . the larger these are, the more quickly your homeworld can start cranking out new fleets.
Starting Ultranium. (Notice that the Mah-Tog race starts with a huge hoard of Ultranium, but almost nothing else . . . this is the race to choose if you want to customize your starting position, because you can afford to buy new licenses immediately.)
Starting fleet. Some fleets have a lot of strength, some have a lot of speed, and some have good transport ability . . . but none have ALL these things. Will you choose a balance, or will you pick a race that's very good in one category and weak in others?
Starting licenses. Every world begins with licenses to produce every kind of unit in its starting fleet, and some have one or two other licenses. Of course, you can buy more licenses, but that takes Ultranium . . .
Special ability. Every race has at least one special advantage of some kind, shown at the bottom of the description with the green arrow.
Other things that will help you choose:
Run a solo (or more than one) for each race you're interested in, just to see how it builds up.
Get into some quick PUB games to see how each race goes against a live opponent.
Look at the Game Information Page for the game you're going to join, and see which races are popular and which ones are not.
Use the chat or the forums to ask other players for their advice. Warning: Some of your fellow players are nuts, and some of them lie! But then, that's why YOU should control the galaxy, and not THEM.