I built my first PC in early 1999, so the parts I used would make it a 1998-era PC. I only had a modest budget of around $1,000, give or take a few $100. So here's what I ended up with:
ASUS P2B Revision 1.02 (i440BX chipset, Slot 1)
Intel Pentium II 350MHz "Deschutes" (100MHz FSB, 2.0v)
128MB PC-100 SDRAM (in a single stick)
Diamond Stealth II G460 (i740 graphics chip, 8MB VRAM, AGP 2x interface)
Creative Labs Sound Blaster AWE64 Gold (8MB RAM, ISA interface)
UNKNOWN 10/100 Ethernet (PCI interface)
UNKNOWN 56Kbps modem/fax (ISA interface)
Maxtor 10GB PATA IDE HDD
24x CD-ROM PATA ODD
1.44MB 2.5" FDD
ZIP 100MB PATA
Windows 98 (first edition)
17" Cybervision CRT monitor display
Powered audio-monitor speakers
The computer lasted me in this configuration for over a year. Played Half-Life, Final Fantasy VII, and a few other games on it just fine. Also had Borland C++ Builder 3, a code compiler on it and it was faster after its build than anything else in the college computer lab. That 100MHz memory speed and FSB speed increase from 66MHz really made a difference in both gaming and code compiling. And I NEVER ran into memory issues with 128MB of memory.
I didn't see 256MB of RAM until I built my second computer after 2002, an AMD Athlon XP 1800+ "Palomino" based system that ran Windows XP, before any Service Packs were released. Obviously, 256MB of memory is awful once you hit Service Pack 2. At that point, I wouldn't recommend anything less than 1GB of RAM, but that came a few years later, when RAM prices had dropped accordingly.
Now, that system above has been reconfigured about two years ago as a retro gaming build. Let's see the changes I made now that price was not an object.
ASUS P2B Revision 1.02 ------------------------> NO CHANGE (just a BIOS flash to latest version)
Intel Pentium II 350MHz "Deschutes" --------> Intel Pentium III 600MHz "Katmai" (100MHz FSB, 2.0v version)
128MB PC-100 SDRAM --------------------------> 256MB PC-100 SDRAM (memory is cheap, so I added a 2nd stick)
Diamond Stealth II G460 (i740) ---------------> Diamond Viper V770 (NVIDIA Riva TNT2 32MB AGP card)
Creative Labs Sound Blaster AWE64 Gold ---> Creative Labs Sound Blaster AWE64 Standard (no longer have the Gold)
UNKNOWN 10/100 Ethernet -------------------> 3COM 10/100 Ethernet PCI
UNKNOWN 56Kbps modem/fax ---------------> REMOVED
Maxtor 10GB PATA IDE HDD --------------------> Western Digital 40GB Caviar PATA IDE HDD
24x CD-ROM PATA ODD -------------------------> 42x CD-RW PATA ODD
1.44MB 2.5" FDD --------------------------------> 1.44MB 2.5" FDD
ZIP 100MB PATA ---------------------------------> ZIP 100MB PATA
Windows 98 (first edition) --------------------> Windows 98 SE (upgraded from the original version that I still have)
17" Cybervision CRT monitor display --------> 27" Samsung HDTV (1024x768 res)
Powered audio-monitor speakers ------------> 27" Samsung HDTV
-----------------------------------------------------> 12MB STB-1000v Voodoo2 3d Graphics Accelerator
-----------------------------------------------------> 12MB STB-1000v Voodoo2 3d Graphics Accelerator
Yes, there's two in there in SLI now. I get the best of DirectX 5-7 with the TNT2 card for games before the introduction of the Radeon and GeForce GPUs (i.e. pre-hardware T&L) and the best of GLIDE back in its hey-day (which I never had before).
My take on the proper RAM amount for mid-1999 gaming rigs would be 128MB. Windows 98 had GOBS of memory space with 128MB and never had any issues, even when doing actual work like compiling computer code. I know I doubled it to 256MB during the rebuild a few years back, but that's because I was going complete over-kill on the system, maxing out the CPU with the fastest available that would work (the P3 Katmai), doubling the RAM to see how web pages would work (Vogons and Google are the only things that work right on Firefox 2.0), etc.