Races are more of a cosmetic choice these days, everyone gets the same stats. They have different starting skills, but the differences are so minor they might as well not exist. Any race can train and fly any other races' ships so don't worry about that.
My advice is to choose race based on what backstory you like and then research the different races' ships and train whatever race you want to fly early on.
Here's a (very) brief overview of the races backstories and what their ships usually does:
Amarr: Teocratic society, slavery practicers, believes they are bringing the word of god to nonbelievers. Largest empire story-wise, allied with the Caldari. Ships usually use lasers and heavy armour tanks.
Caldari: Corporately controlled society, the mega-corporations own everything. Fond of anything high-tech. Smallest empire story-wise, allied to the Amarr. Their ships use shields for defence, missiles and railguns for offense. They generally have the slowest ships in the game.
Gallente: Space federation, not much more to say. They think they are New Eden's last bastion of liberty and freedom and do not hesitate to spread their ideals. Second largest empire story-wise, allied with the Minmatar. Ships use armour tanks and drones and hybrids (railguns and blasters) for offense.
Minmatar: Tribal newly built society. Were slaves under the Amarr for a long time, rebelled and broke free. Second smallest empire story-wise, allied with the Gallente. Ships use either shield or armour tanks (depending on ship) and both missiles and projectile turrets. Mainly projectile turrets though. Fastest ships in the game, fond of hit-and-run tactics.
This is woefully incomplete, the backstory of Eve is massive, and If you're interested I strongly recommend at least looking at at least some of it. I also think the character creator has some more info on each empire and bloodline.