Got Wesnoth? (Score 1)

The Battle for Wesnoth (http://www.wesnoth.org/) is an open source, turn based strategy game with binaries available for linux, windows, mac and more. It has a nice wikipedia page http://en.wikipedia.org/wiki/Battle_for_Wesnoth, if you'd like to have a look-see. It addresses each of your three points nicely I think.

It is pretty much the ONLY game I have been playing since I discovered it seven months ago. It is easy to jump into and VERY HARD to master. The multiplayer community is vibrant, and international.

See for yourself!