but you might as well buy a router/modem combination. Your wife's laptop will need either a PCMCIA card-type wireless adapter or one of the many external USB adapters that are available - don't worry about make, there will be no compatibility issues.
You can either leave your PC connected to the router via the cable that will be supplied with it (for setup purposes), or you can go wireless as well, and install a PCI card adapter, or a USB adapter. If you opt for USB adapters make sure you run the software first, before you plug in the adapter.
Once the router is up and running you can access the internet via either of the computers without the need for the other one to be on.
When you're happy that all is well, give some thought to securing your wireless network - there will be instructions with the router.