Access Point Setup

I have a router downstairs, and I connect to it from upstairs via a wireless adapter. But this Christmas I am getting an Xbox 360, and I am going to try to get Xbox Live. I was thinking about getting an access point (link), putting it upstairs, then get a wired router (link), and connect my xbox, xbox 360, and my computer to it wiredly (is that even a word? lol). This is how my wireless network is setup:

Downstairs: Modem connects to cable line and phone line. Router connects to the Modem through Ethernet port. Downstairs computer connects to the Router through an Ethernet wire.
Upstairs: Computer has a wireless adapter which connects to Router.

I may be wrong on how I set this up, but I was thinking it goes like this:

Upstairs: Access point connects to Router wirelessly. Wired Router connects to Access Point through Ethernet port. Xbox, Xbox 360, and computer connects to the Wired Router through Ethernet wires.


Am I correct on how to set this up?
Also, should I use this setup, or just get the Xbox 360 wireless adapter? Upstairs doesn't get that good of a connection, just to forewarn you.

Thanks.