Earth Alliance: Slow, unmaneuverable, but tough and good fire arcs and lots of fighters. Also more interceptors than you can count.
Narns: Slow, unmaneuverable, excellent fire arcs and E-Mines to trash any and all fighters
Centauri: Superb mix of ships varying from very fast manueverable attack ships to long range heavily armed cruisers. All quite tough and insanely good forward firepower.
Minbari: Less guns than most others but those they have are VERY nasty and long ranged. Ships are also a weaker than most others but protected by evil stealth systems. I love em personally but some people think theyre unbalanced so be warned (I wll say though dont form your oppinion on them from your first game against em though as there are lots of tricks to learn)
Interstellar Alliance: Wouldnt really recoment them as a beginner fleet as they mainly depend on Whitestars, which while DEADLY if used right can be ripped to shreds if you dont know what youre doing with them.
Shadows: Very maneuverable, Nasty long ranged turreted beams of doom. BUT... relatively easy to kill if youre not careful. Deadly if used right but NOT a beginners fleet again.
Vorlons: Less maneuverable than shadows, but a bit tougher and more guns (but forward firing). Again potentially lethal but you really have to play them right... (The Vorlons are quite hotly debated alomst as much as Minbari stealth)
Drazi: At first glance all you have to do is charge screaming and firing but if you just do that, chances are you will lose. Small individually quite crappy ships. But soooooo many of them
Havent played/played against any other league races but from what Ive seen:
Vree: Maneuverable as hell, EVIL weapons that make mincemeat out of enemies, Armour made of genuine recycled paper....
Brakiri: Bricks with many beams.
Abbai: Not all that deadly offensively by comparison to some but VERY VERY tough ships (excellent hull, more interceptors than ANYONE, even EA).
Raiders: Theyre raiders. Theyre ships are quite poo. But they can take lots of them. And 9 billion Delta-V fighers.