To add -- there is nothing that corresponds to a "normal" MMO's "class" system in EVE.
When you start out, it's akin to saying (in a Fantasy-style game) that you're a "Grey Dwarf" or "Deep Gnome". As far as the game is concerned mechanics-wise, you're a "Gnome" or a "Dwarf", and are then only limited to things a Gnome or Dwarf can wear/use (e.g. "Small" weapons/armor, if they have a size-limiting scheme). Note that in said fantasy-style game, a subrace may have different attributes (+1 INT, -1 CON, etc) than the base race, which doesn't hold true for eve anymore.
When you're thinking of your "class" in EVE, it's dependent on which ship you choose to fly AND how you choose to fit it. For example:
Navitas(Gallente Frigate Logistics ship), with Remote Armor Reppers= Cleric (i.e. healer)
Rokh(Caldari Battleship), with Railguns ("long range" guns) = Ranger (i.e. long-ranged/sniping combat)
Oracle (Amarr Battlecruiser), with Pulse Lasers ("short range" guns) = Fighter (i.e. close ranged fighting)
With that said, those are the "general" roles, and there's nothing stopping you from fitting a Remote Armor Repair module to a ship, though it will be less effective than using a logistics ship (because the logi ship is built from the ground up to be a "healer"). This is kinda like having your rogue/theif hold on to a few healing scrolls to use in case your healer gets put out of commission (killed, distance, any other things that keeps them from casting spells).
The best part with the "class" being tied to the ship, rather than the character is that you can swap you class in as little as 60 seconds (less if you have a fast computer/internet connection) just by docking up and switching what ship you're in.
There is also no limit to whose ships you can fly (with a few caveats). Got tired of looking at golden ships ... well, train up Gallente. Fly with a corp using mainly shield fits, then train up Caldari or Minmatar (preferably Minmatar -- Trust in the Rust!
). The only real caveat to this is that each race has a different primary/secondary weapon system and tank preference, so it's generally a "good idea"(tm) to stick with one racial ship lineup for a little while, at least til you get your core skills up and burning a few days training these "cross-race" skills won't leave you gimped.
Race -- Primary/Secondary Weapons -- tank
Amarr -- Laser Turrets / Drones (some missiles too) -- Armor
Caldari -- Missiles / Hybrid Turrets [Railguns] (few drones) -- Shields
Gallente -- Hybrid Turrets [Blasters] / drones -- Armor
Minmatar -- Projectile Turrets / missiles -- Depends (Minnie happen to be the most mixed race)
For Caldari and Gallente, they both use the Hybrid Turrets, though Caldari ships generally have bonuses that better apply to railguns (i.e. range, tracking), and Gallente bonuses generally better apply to blasters (i.e. damage). There's nothing stopping you from making a Blaster Rokh or a Rail Brutix though.