yes, basically you need a wireless router.
b, g and N are the different speeds and sometimes range.
N is the latest and fastest, for streaming movies and such.
They are all backwards compatible.
G is good enough for surfing the web and some movies. Since it is "last years model" you can get some okay deals, but since people are gearing up to build N, you can get some pretty good deals there too. Just saying you have options.
The wireless router should have regular ether net ports in it as well. So you can plug the cable modem into the router, your regular pc into the router and then let everone one else work wirelessly.
You have a couple of choices in getting the other desktop on the wireless network. They do make cards you can insert, they make USB adapters, and they make an item called wireless network adapter that lets you plug it in via normal network cable. Most times the USB version will be the cheapest way to go.
While a lot of laptops have wireless built in, not all do. You will have to check your specs.
As for range, you will just have to check. you could put up a repeater, but just depends on how far away you really are. Most times I can see 4 or 5 other house's networks in my neighborhood.
As for seeing on the other machine, you will be on the same network, so anything that lets you do that should work. The only issue is the only tools I can think of bump the other person off the machine when you look in. someone else may know a better desktop sharing program. Net meeting works, but they have to acknolege you looking.