Excellent idea!

Have you considered developing in Unity? (http://unity3d.com/). It's one of the most popular multi-platform game engines now. It's usable for 2D as well and one code will work everywhere including browsers, desktop, facebook and mobile devices. Other popular choice around professionals now is LibGDX (http://libgdx.badlogicgames.com/features.html)

But anyway you will need some server programming as well. Such games are always front-end (any engine like these or just html5) + back-end (server side, where all DBs are kept).

3 weeks sounds too much optimistic for the first real alpha version even with minimal functionality. Such projects always take more time than we think in the beginning.

It's very important for the developers to plan all future architecture in advance before actual programming. Otherwise you will build a house without a basement and after that will need to repair and repair it each time when adding new functionality.

Other popular conception is to build a simple prototype. Three weeks look real for it. Test it for playability and after that plan and build a new concrete basement for the real game. If there are enough people in a team both tasks can go simultaneously.

I wish you success with such a great project and will be happy to beta test.