Noticed there's a few guys having issues getting setup with their new NetUSBee devices, so figured I'd post a few easy-to-find hints to explain what I managed to work out.
Basically I followed the instructions here: http://hardware.atari.org/sfl/index.htm, though I didn't change my PC config (as per step 4) and gave the Atari an IP of 192.168.0.101 since my router sits on .0.1.
Then I needed to manually edit the STing routing table, which I laid out like so (I think from memory the filename was routes.tab):
<Atari IP> 255.255.255.0 EtherNet 0.0.0.0
0.0.0.0 0.0.0.0 EtherNet <Router IP>
And finally I needed to specify a DNS server IP in the main STing config file, which I think is default.cfg, but again I'll double check. Find the line for NAMESERVER and set it to 8.8.8.8 or your preferred server. Once I'd done all that I figured up AtarIRC, it resolved the server correctly and I was online!