you can start off with the newer ones, which are some of the most fast paced shooters out there
but if you want true challenges
Call of Duty 2: it is fast paced, though more tactical than the newer ones by not having the ability to sprint, the weapons cannot be modified and there are no kill streaks either, nor Perks
now, if you want to be a tough son of a *****
Call of Duty and Call of Duty United Offensive
the very first one and the expansion pack, you see, this is the most primitive of the series, it has no health regeneration at all, you can't sprint, weapons cannot be modified, and the grenade (frag only) is on a different weapon tab, that is, you gotta select it before using it, instead, it allows you to carry 3 weapons and the grenades, the weapons would be, uh, for example: an SMG, a Sniper and the pistol
this Call of Duty isn't as fast paced, but it's the most hardcore of the whole series, by having you think your actions properly, if you get shot, you will not recover until you kill someone and take their medkit
though it's PC exclusive
still they're great multiplayer experiences, and there's lots of people playing them, so I recommend you picking them up, they are quite cheap nowadays
also, they have kickass campaigns, especially CoD 2's Russian campaign
remember, this is just my opinion, mostly because those are my two favorite FPSs, you may or may not like them, I'm just giving you some extra options, just for the hell of it =P
then again, I'm more of a classic guy