Seeing as its not going to be something where speed is hugely important (e.g a 3D shooting game) you have a lot greater choice (you could use java, .net, whatever) whereas if speed was important you would be limited to something like C++.

I made a blackjack game once that could be played across a network. It was written in VB.NET (.NET is quite good for networking)

Java might be quite a good idea. I dont know how good its networking is but java is croos-platform so it can be run on OSX, Linux etc... too