So far, I have not needed to change much about my build, except the following:

I added a DVD-ROM drive, not sure of the speeds, but it is fast.
I added a Seagate Barracuda 20GB HDD to it. It is very quiet, whereas my old Quantum Fireball 6.4GB was very loud. This computer, with its new fans and quiet hard drive, actually rivals my main computer in terms of silence. It is honestly ridiculous how quiet this 1999 PC is, and I love it.
I changed the heatsink on my TNT2 card out with one from a PCI FX-5200, and so far it seems to be working great. I used Arctic Silver MX-4.

The main point of these upgrades was to quiet the machine down, give it some more storage space, and give it some better cooling ability.

The outside of the PC is the same, but here's the new look of the TNT2:

The DVD drive is from 2001, and the hard drive is from roughly 2002, however, these two items add functionality to this system and improve it enough to where I am happy with them being there. Most computers I see with a Pentium III 500 in magazine ads back in the day show ~18GB HDDs, so this HDD is right up that alley, only that it is newer and doesn't make ~600db of racket while it's on. It also should be much faster than the old HDD, so I'm looking forwards to a few performance boosts with it being ATA-IV (as it says on the label), even if it's constricted by the motherboard's ATA-33 bus.