...and I'm in no way qualified to be anything more than another voice in the din.
I run a P4 1.7, 512 RDRAM Dell 8200, originally with a GeForce3 64 meg card.
Had no end of frustrations and problems -- literally couldn't get past the first turn... slow downs, freezes, CTD, etc. Seemed pretty obvious- based on the fact that even CTD and freezes were proceeded by obvious issues in graphic rendering - that I needed more graphic muscle.
I added another 256 of RAM and move to an ATI 9000 card/128 meg.
Had more success -- I'm having driver problems with my new card (got a discounted open box with no disk and ATI doesn't seem to offer the original driver on their site). My system thinks I'm running a geforce4 mx420 now - and Civ disables a lot of the graphics (virtually all animation is gone).
However, on the plus side -- have been able to play a bit with no crashes.
Soooo.... and this is just my lonely ol' opinion.....
I really do think you need a minimum 128 meg card, with all the T&L/pixel shading bells and whistles.
Maybe later tonight, I'll see if adding another 256 of RAM was really necessary, but put me squarely in the column of those believing that a 128 meg gfx card should be considered a "minimum requirement", not a rec'ed requirement. There's a sticky at the top on cards/T&L/etc that's really helpful, as well as another good card Q&A thread that was informative, too.
Like I said -- in no way an expert -- but I really do believe the vid card is the key.