Wondrous news!
The good: This is now a Windows 95 gaming computer, because 98 was just too damn unstable on the machine for some reason. Lucky for me, this doesn't rule out any of my baseline games (the list I had in the first post), and may affect only a handful of the ones suggested here.
The bad: I can't find sound card drivers for this. I might need to purchase a new sound card, and I have decided to wait for the video card to arrive in the mail before I do any further toying with expansion slots. Hopefully it'll be easier if I do buy a new sound card, because I'll know exactly what I'm getting (and if I shop effectively, maybe even a driver disk to save me some time). The current card was a Creative CT4790 (which is of the Sound Blaster series, but I don't know if it was Live, Live Pro, 16, or AWE-32, and googling tells me absolutely nothing).
The ugly: PCI bus error on POST, starting with the second Windows 95 bootup since this project started. I don't know why it started, but since I'll be removing pretty much everything from the expansion slots when the graphics card gets here, it should be a problem that should be of little importance.
The extra: I don't have to buy speakers, I just dug up an old pair in the pantry (of all places to find some).
The postmortem: Don't ever, ever, ever expect a project involving archaic, old hardware to take you a week to complete. This will likely span into next week for me due to school, but since this is something I can literally feel my way through on the as-I-go basis (considering the first computers I ever repaired were of the Windows 9x/Intel Celeron/Pentium MMX/2/3 generation), it might be easily completed even sooner than that.