Solved it.
In case anyone wishes to try this, the procedure, largely following this (
http://www.nextcomputers.org/docs/FAQ-OpenStepOnEmulators.pdf) PDF, is:
1) Set up your VM with 256 MB of RAM, 64 MB of VRAM, a 4 GB drive and 1 CPU. In Parallels 7 You can leave all of the performance/VT-X stuff on;
2) Install Openstep 4.2. Install the 4.2 patch;
3) Install the NE2K driver;
4) Shut down. Under Boot Order, make sure the hard drive is the first device, and add "devices.net.force_adapter_type=rtl"; in the boot flags. Change the network to Bridged Network and make sure you select your actual, active ethernet port. Mine is en2. Restart;
5) Open HostManager.app. Under Local choose "use local domain only". Let the machine Restart;
6) Bacn into HostManager.app. Set all of the various options as if your VM was a real machine on your network. I assigned 192.168.2.150 as the machine's IP address;
6) Reboot and install OmniWeb. Surf the web!
For those wishing to use VirtualBox, the procedure is almost identical. The only real difference is that VB uses the standard AMD PCI network driver, so you don't have to install the NE2K driver. However, VB won't do full screen.