Matt, you need one service provider and the router will NAT (network address translation) you and your buddies addresses and it will be routable via the IP address assigned by your provider.
The "g" is a standards designation. The IEEE makes standards for networking protocols (and other things too) that vendors in the network market have to follow or their shit won't work with other vendors shit. 802.11g is the wireless standard for, essentially, 54Mbit/sec wireless. 802.11b, that I mentioned before, is the 11Mbit/sec wireless standard. There are other wireless standards, but most people don't follow them, or they are really old, like 802.11a which was 2Mbit/sec.
Anyway, if you buy a wireless router (the ones you are looking at are commonly called 54g routers) you have to have a wireless card/chip in your PC/laptop or it won't work.
If you don't care about security, then anyone within range of your wireless router can get on your wireless network and use your network connection for free. If you do decide that you want some sort of security, make sure that whatever router you buy will work with whatever kind of cards you have for a connection. I had to replace two cards in two PCs when I went from WEP to WPA encryption because the cards didn't support WPA. Not a big deal, but it did cost about $180 for the 2 cards.
Of the 2 routers you showed, the Netgear will allow for 54Mbit/sec while the Linksys will only allow for 11Mbit. Unless you are transferring assloads of data BETWEEN you and your friend, I would just use the Linksys. It will be cheaper, the cards for your PCs will be cheaper (or you can buy 54g cards and it will still work) and Linksys is an ASSLOAD better than Netgear when it comes to people that don't know all of this shit.
I hope that helps some. If you need more help just ask.