You will need a wireless router. Just set it up according to the manual. The desktop will connect as per usual to the router, but is using the WAN port if it's going to be a wired connection. Otherwise, it will have problems accessing the Net.
Securing the network wise, WEP/WPA is present for most routers. Some include WPA2. WEP still offers some sort of protection, but it's too easy to crack, in a matter of hours. WPA has several enhancements over WEP, but it basically works the same way as WEP... so it will be cracked in the same way as WEP.
WPA2 is not offered in Windows by default, and you will need a patch before you could use it.
. Note: This link is for XP. I'm not so sure for Vista if you are using Vista.
If you intend to use WPA/WPA2, you will use WPA-PSK or WPA2-PSK. The other options are for enterprise users, of which normal users can't use as they have no server to authenticate with. PSK stands for Pre-Shared Key. Before connecting to a network, you will enter this key (which is like a password). If it's correct, you will be connected to your network.
If you would like your desktop to go wireless as well, you will need a wireless card (usually PCI) or a wireless adapter (usually USB). You need to get the right one. If your router says it supports 802.11B/G, you need to get a card or adapter that does so. Getting a 802.11A card will not work with your router, simply because it uses another frequency. For PCI cards, you will need to install the necessary drivers before it will work. You will need to check the manual for the instructions and follow as stated. Doing the reverse doesn't help.
Speed wise, what is stated as the maximum theoretical speed, you will never get it. Theories are theories. In reality, you can expect that the speed is around half of the theoretical speed stated.
When you use it for surfing, it will be capped by your ISP, depending on your plan. Say you have a 1Mbps broadband plan, that's the maximum it will go. It will not even be half.
Wireless surfing tends to be slower than their wired counterparts because they can only be receiving or sending at any one time, not both.
You don't pay for the varying speeds in wireless routers, but your ADSL plan.
One thing, don't get a Linksys router. As much as they are easy to use, they are very unstable. Not that I hate it, I used to like it. But with each firmware upgrade, it causes more problems than needed.