I've been through this same process, and taken it about as far as I could. There is another thread somewhere on this forum where I discussed it, but to save you having to hunt through the forum, the answer in brief is:
No, Civ3 will not run under Wine.
Nor will it run under CedegaCVS (ie the downloadable version).
It *will* apparently work with the commercial version of Cedega. (but I haven't actually tried it).
The reason for all this is that Civ3 uses DirectX for its graphics, which Cedega uses, but needs to pay a licence for, so it only comes with the paid version.
It is a shame, because I really enjoy Civ3, but not enough to spend more money getting it to work.