When that motherboard was new, 10/100Mbit ethernet was less than 5 years old and still expensive, so there is no way they would've included such a NIC and at best you would've got a 10BT or 10BASE5 onboard (10Gbit ethernet has been available for 10 years now and you don't see them included on too many new boards yet). The serial ports are there for you to hook up an external modem to dial-up to AOL and access the internet that way (hey it was 1999).
If you've got to get a NIC anyway, get a dual-port one and you'd be able to use it as a router, booting off a floppy or CompactFlash card. It has enough CPU power to rout 100Mbps WAN service and doesn't really use much more electricity than many modern routers. Heck I've got routers that came with a 60w power brick!
While it does have USB 2.0, using limited CPU power to poll a USB WiFi device sounds like a bad idea. This was an era when hardware accelerated sound cards could reduce the load on the CPU (a feature which was made impossible with Windows Vista except in OpenAL).
And yes, not all AGP slots had the latch. Without it the little L-piece just stays outside of the slot. BTW that looks like an Aopen MX34 board in case you wanted to look at the manual.