I get nostalgic about the good old days when I was happy as a clam playing Civ1--watching the little Phalanx completely destroy a modern Battleship and come out of it without a scratch. Ah, the days before health bars.
I don't play Civ2 much because well, to be honest I was never all that obsessed with it as a game (the Civ1 buzz had already worn off). What got me hooked was the modding (i.e. scenario design).
And considering I'm still in the process of working on a total conversion of it, I'd say it isn't nostalgia that keeps me here but actual interest in a product that's so easy to work with (minus the AI...ugh), relatively speaking; working with Civ2's simple events/rules is orders of magnitude easier than working with Python/XML in Civ4.
Civ3 is nice but quite limited (namely due it's lack of player scripting; i.e. events). Nevertheless I'm working on a similar epic conversion for that as well (for similar reasons). Should be quite good when it comes out...which should be about the same time Civ7 hits store shelves.
)
As for FreeCiv: nice effort but not particularly impressive as it presently is. Lacks moddability (it is itself still an unfinished project).
If it's just the vanilla game you're interested in, then there really isn't much of a reason to play Civ2 (nostalgia aside).
Your rig should be good enough by now to play Civ3, which is basically just a better Civ2 with some minor controversial changes. If you have a higher-end rig, you might as well skip Civ3 altogether and go straight into Civ4. Just be warned: you may need to take a programming course and quit your job in order to make a scenario for it (i.e. beyond just editing maps and a few unit stats).
Right now, I'm in my Civ2 mode so I'll pop in here now and then and work on the Civ2 stuff until I get tired of it--something that happens fairly quickly whenever I try working with the AI.