There isn't a difference in range (that I know of) between 802.11B and G. The difference would be in the hardware itself by the manufacturer. (Different ones have different ranges) Since price is an issue and you want it basically to share a DSL connection, 802.11b would be perfect for you. G is only necessary if the main intent is to transfer files fast between computers.
Regarding cheap routers/PCI card adapters - basically just take a look in the local electronic store ads (BB, CC, Frys, Microcenter, etc) - since you're on a budget cheapest is probably the way to go for you. There's no discernible difference really between brands, although lots of people have different things to say about different brands. (I had lots of trouble with my Netgear. Right now I'm using a combo of Microsoft wireless router and Siemens USB wireless adapter)
Regarding the PCI adapter - your reception may suffer a bit if your computer is in an enclosed space. I'd recommend a USB adapter just because you have the option of being able to move it around for best link/signal strength. I don't know how your house is setup, how far away the wireless computer will be from the router, and what type of building materials the signal will have to go through (since it's going to a basement). In general 50ft would be the maximum length I'd recommend if you're going to use a PCI adapter. (This is just a general statement though)