If you are looking to buy a product based solely on your desire for multi-player, I would tell you to run, not walk, away from Civ V.
As has already been pointed out, the active community size is quite low. You can easily get a sense of that by just looking at how many new threads get started in this forum that are about problems vs. people discussing strategy and how much fun they have. If your main opponents are going to be people on the Internet, you will run into the lobby problems that Spider brought up. There is also what is (for me) intolerable lag in every single game I've played. In a turn-based game, I expect the online lag to be near zero, however, Civ V has worse lag than any RTS I've ever played online going back to 2000. If the turn timer is enabled, there are times I can not even finish my moves for the turn due to the lag. For this reason more than any other I've stopped trying to play this game multi-player until some patches come out that attempt to deal with these issues. As I assume this is a low priority for them, I may never come back since I'll be playing a more enjoyable game by the time they get around to it. Note that Firaxis just recently started advertising to hire multi-player programmers, so that also does not leave me confident anything will change in the near future.
If you are only going to play with friends over a LAN, you may not run into these issues, however, some people have reported lag issues still persist even in a LAN environment. Without knowing all the details of their network setup it would be hard to say how prevalent this problem is. Even with no lag, user-created content is not yet available to be used in multi-player, so if you and your friends like to share maps or mods, you can't do that, either. Combat animations are also always off; some people really don't like that since if you didn't happen to have the battle right in front of you on your screen, it can be unclear how and where you were attacked. Despite all this, there is a hardcore group that still keeps giving it a go, so you can probably find some games with them (maybe Canuck Soldier can reprint his Steam channel link in here).