Manuel, in windows xp you can simply turn internet connection sharing on from your main computer and that will then allow any other computers on your network to access that connection.
Here's some definitions I've managed to assume:
Switch - box that will take many inputs for wired networks
Router - a switch with a built in firewall. sometimes also includes a wireless access point.
Wireless Access Point - you can think of this as the antenna that would connect to your main computer.
The simplest thing for you to do is to connect a wireless access point to your main computer and then a reciever on your second computer (possibly use USB on this).
There's no reason to use 802.11a or 802.11g since even broadband connections are slower than those transfer rates. Stick with 802.11b (wi-fi) for the price and because you really don't need anything else.
Although my information not be extremely accurate, it's what I've picked up here and there. I hope this is of use to you.
I currently own a Netgear Wireless Router that I purchased from Amazon for $40. I have my desktop wired to it and my laptop has a PCMCIA wireless receiver on it. The broadband connection plugs right into the router.