Doesn't take long to figure it out. There are four core groups imo. Medic, Engineer, then the grunts (Demo / soldier / Heavy / pyro), then the rest. All classes have limited weapon choices. One melee, a sidearm, then the main weapon.
Medic is on its own, you need a medic and a good one to get anywhere. Engineers are important for teleports and controlling areas, grunts provide the cannon fodder, the rest (sniper, scout, spy) run interference.
You can limit yourself to popular maps on constant rotation. Payload (goldrush, upward, badwater), attack-defend (dustbowl, gorge, gravel pit), and Control Points which I'm not a fan of (granary, badlands, well).
Fave maps would be cp_dustbowl, pl_goldrush, and pl_upward. The Dust2 of TF2.
TF2 is free, so why not just give it a go. Start with soldier, heavy, pyro, sniper, straight forward point and shoot classes.
I love L4D/L4D2 as well. Not a fan of PVP but I love the coop, except I've played them to death now. TF2 has more depth.