I'd get an 802.11b adapter and an 802.11g adapter. I would plug the g adapter to a computer that is on all of the time, and turn on internet connection sharing. Then I would plug the b adapter into the old USB 1.1 machine.
USB 1.1 is limited to 12Mbps, so and 802.11g adapter operating at 54Mbps would be bottlenecked by the inteface. But they are so cheap, you may want to get g just for the range.
There are other ways to do this, but this is probably the cheapest, aside from wired.