I don't even categorize it as a normal shooter. nothing else really compares to it from this generation of fps. Its not all about head-shots or remarkable twitch skills (though they can help quite a bit in certain scenarios)
it's all about teamwork, as well as strategy to a degree. you don't need to be another Patton to have to be able to succeed, but you don't need to be MLG-level either. just simply understanding class dynamics and working together accounts for a lot.
As for classes, what other game lets you use giant chain guns, grenade launchers, flamethrowers, rocket launchers, and other crazy gadgets as main weapons? I can't really think of any true fps that has that. Class diversity makes the game easier for new players and more interesting at higher levels. each class has it's strengths and weaknesses, no one player can completely dominate everyone else. Also, you don't have many elements for "cheap kills" like battle rifles (my opinion), spammed grenades (valve design philosophy), and noob tubes (without a doubt the most frustrating weapon of all time, no argument)
while fps have been going more and more for reality, tf2 goes in the opposite direction. It's characters are designed not only to be interesting and funny, but also recognizable. you know who's got the machine gun and who's got the flamethrower. it makes a surprisingly large difference.
Ultimately, I think TF2 is one of the best fps games around. by far. You don't hear many people hating on TF2. it actually balances out with relative frequency, and makes it a priority to update content pretty frequently. It rewards teamwork lucratively, and encourages new players by making them a part of a larger operation. It's also an fps developed for the PC, and is thus inherently superior to anything put out by a console by edict of the Supreme Being.
So yeah, play it. its what, 15 bucks? you don't need to subscribe for it, it can run on almost any machine. just get it already. you won't regret it.