Linksys makes good networking products. However, in my experience (which is quite extensive) the range on their 802.11b/g products has never been very good. I eventually replaced my own Linksys wireless router with a Netgear one and it solved all of the connection problems we had been having on the basement computer. Previously, we had replaced the Linksys wireless device the computer was using with a different brand, and that helped quite a bit.
Basically, I'd recommend Netgear based on my own experience. I've used one router and one 802.11g USB device, and both work extremely well to this day.
As for the standard, I'd suggest you just stick with 802.11g, because quite often the 108mbps devices have problems. In fact, most of them do from what I've read. However, TweakTown actually had a very good review of one a while ago. If someone pulls it up, I'd suggest you use whatever product that they reviewed. The extra speed will make a pretty big different for the file transfers you'll want to do. However, if I were in your position I'd save my money and stick with G.
As for extending your range, it can certainly be worth it or, more importantly, necessary, but here's what I'd do: First get everything and try it. If you get unreliable connectivity, then you make your own antenna, or cantenna, I should say. Go
here if you end up needing this.
If you need to get a wireless device for your machine (and by the looks of it, you don't), I'd suggest you get a PCI card with a removable antenna, because it makes using a different one much easier. If it's a laptop, then you'd obviously have to go with USB or PCMCIA.