It's a matter of choice. If you like flexibility laptop will be better for you. If you do not mind to have your computer at the same place desktop will work for you.
Buying a wireless card depends on if your wanting to use the laptop while not near the desktop. You can buy network cables to connect the two computers as well.
You do not have to use wireless for all of them. You can connect your desktops using cables. And use your laptop with built-in wireless adapter.
If you are talking about building of wireless network. Then you need a wireless router and a wireless network adapter (if you have a laptop you might not need it). If you have a desktop you rather will have to purchase a wireless network adapter. Pay attention to what kind of wireless network you are going to build. It can be a, b, g, and n types.
There are various types of wireless modems. A wireless antenna will connect you to a wireless network, while a Ethernet cable simply connects from desktop to modem. To obtain a digital version of your wireless manual, contact the modem manufacturer by phone or e-mail.
Fiber
Have you checked that the both are set up for sharing? Do the two machines have the same domain name?
Your router should have a wireless network. Read the manual for how to enable it and set up a key, then connect to it with your laptop. Or just use a cable like with a desktop.
Yes, This is for adding a wireless antenna to a desktop or laptop computer that does not have wireless built in. You still need a wireless router connected to your internet provider.
You must first purchase and install the required hardware. The wireless router which is connected to your desktop by cable, and Wireless network adapters for each device on the wireless network. Newer laptop computers have wireless adapters built-in . Separate USB adapters must be purchased for computers that don't have that built-in capability If you use Windows XP, then run the Home Networking Wizard. Go to Start/My Network places/ and under Network Tasks click on "Set up a Home or Small Office Network". This launches a wizard that will guide you through the process. You must run the wizard on the desktop computer first. At the end of that process, you will be told to make a copy on removable media, such as a CD, and then run the copy on the laptop. If you're not running Windows XP it can be a little different.
Wireless network adapter.
Set up a network.
99.9% of modern laptop have both wireless as well as wire network interface.