If your to start off small first of all it might be an idea to make a simple 2D above view version of it where it doesn't use any internet connections. So both players take turns to use the same PC to make their moves, after all it is a game that is turn based so using the one PC is ok.

Depends how you want to do this game I suppose for the graphics, if your willing to learn some basic DirectX stuff (www.DirectX4VB) then you can make a fullscreen game. Or if your new to VB then it might be a better idea to use simpily a PictureBox for each object (BitBlt if you want, would be better too).
I would go for the DirectX approach as it will run faster and look nicer, allows you to advance the game to 3D if you decide to update it.

Back to this simple version first, this will not focus on graphics too much because there will probably be a lot of code needed to get the whole Monopoly thing working.