Here is the first problem with your set up idea, you need to connect the access point to the router, or switch with and ethernet cable, and then connect to other computers wirelessly. The way that you described it you will be connecting the computers to the access point with an ethernet cable, which won't work.
That being said you won't need two access points unless the other two computers are very far from each other. With the two access points being wireless, I would recommend getting something like a wireless USB adapter. They are pretty cheap and are easier to install then a built in card for the desktops.
I also sounds like you want to set up a windows home network which is a great thing, unfortunately I don't have any experience in setting them up. But if you google it or visit www.microsoft.com
, they have good directions, I'm sure. They should be able to help you with setting up a print server too.