1) Ensure you properly installed the drivers for your Ethernet card. If you can get drivers from your card's vendor, those might be better than the generic Apple network drivers.
2) Since you're using 7.5.1 and have 8 MB of RAM, I highly suggest installing OpenTransport. It's much easier to configure than MacTCP and has better compatibility with modern routers. You can download OpenTransport 1.1.1 and the update to 1.1.2 in floppy format from the Apple site:
OpenTransport 1.1.1:
Disk 1 -
Disk 2 -
Disk 3 -
Disk 4
OpenTransport 1.1.2 update:
Disk 1 -
Disk 2 -
Disk 3 -
Disk 4
3) After installing, configure OpenTransport to use DHCP (should be enabled by default) and go into the advanced user mode to have it always enabled (instead of TCP/IP only being enabled when it gets used, as it is by default). You can set OT back to simple user mode afterward.
4) Install Netscape 2.02, which is IMHO the best browser for the IIci. It runs nice and quick, while still being fairly compatible with most modern sites. Netscape 3 will also work on a IIci, but it is slow as molasses. Also, 8 MB of RAM is probably not enough to run NS3 stably.
Here's an archive of ancient Netscape releases:
link
And for your convenience, here's a direct download link to Netscape 2.02 English for Mac:
link
That download is too large to fit on a single floppy, so you might have to work some file splitting magic to transport it onto your IIci.
5) After starting up Netscape 2.02 for the first time, quickly press the Stop button to prevent the browser from loading the default Netscape homepage (and all sorts of hell breaking loose). Go to the settings menu and set a blank page as the default site.
Then go to Security settings and disable Javascript. Javascript in NS2 is outdated and produces gazillions of error messages on most JS-enabled sites. If you want to have any kind of fun with your browsing experience, you'll want to disable Javascript.
Finally, don't forget to click 'Save settings' in the settings menu. Otherwise, the default settings will be restored on the next startup.
If all went well, you should be able to produce something like this: