What you need ?
- to play MP you need both Civ3 and PTW or C3C (Conquests). Conquests is better since it already includes PTW so by all means buy C3C (or complete as I think it has both Civ3 and C3C). Anyway Civ3 by itself is not enough.
Civ 3 MP ?
- PTW was buggy, C3C is a little better but not great yet.
Civ 3 is not the best online game.
Finding opponents and games ?
- You can use the Gamespy lobby to find games. Now it is rare to find a game that will last and with dedicated players. The best is to have a group of friends and meet at regular times or join myleague.com as then you can find serious players.
Nevertheless these games are not epic-like. Usually they rely on special set of rules, early combat and therefore civs with early UUs and most last about a hundred turns.
If you want to play a normal epic till modern age, better find a few friends and play at regular times (you can quit, save then reload at a later date). Possible but difficult.
- An alternative ?
A good alternative if you or the others cannot commit for say playing two hours every other night, is to try PBEMs. PBEMs allow you more time to plan your action, you can play epic-like or scenarios to the end, if someone drops you can get a replacement and you can play at the time you prefer even if your fellow players are in a totally diferent timezone.
Now of course, especially for epics, these can last a very long (7 months to finish a Rise of Rome scenario) time but you can play different ones at the same time.
Edit : PBEM thread (as you can see it is much more active than th general MP thread) :
http://forums.civfanatics.com/forumdisplay.php?f=90