A 'badass' system is generally one focused on one specific goal. The biggest problem here isn't even that you're trying to start with a low-end system, it's that you're trying to make it do everything, in particular the things it's not inherently good at, i.e. DOS (no ISA) and also Win9x gaming. I'd suggest choosing something very specific and optimizing for that.
By comparison, I've done something similar with a Packard Bell uATX system, but I'm only focusing on WIn9x (I have other systems for DOS) and moreover my system has onboard Voodoo3, which beats integrated GMA. So I've gone crazy and increased CPU to a P3-1400S (and yes, that means OCing the BX board to 133MHz FSB) upgraded to 512MB CL2 PC133 RAM, added a SATA controller and a 32GB Intel X25E SLC SSD, added an Aureal2 sound card and a NIC for networking. Externally the only thing that gives away it's not the same sad PB Club system is that I replaced the FDD with a ZIP drive. UT99 flies on that system.
Now, that motherboard would also have made a great DOS system, as it has an ISA slot and Voodoo3 has good VESA SVGA support. But if I chose DOS the 1400MHz CPU would have been a disadvantage (much too fast, more need to slow down). Also the ISA slot is shared with one PCI slot, and the Aureal2 and onboard SB64PCI are crap in DOS so I would probably have had to lose the fancy 3D sound and instead use an ISA sound card that wouldn't add anything significant in Win98. Or I'd have to dump the SATA controller and go for PATA-SATA adapters instead. The end result would still have beaten the original system in both Win98 gaming performance and DOS features/compatibilty, but it would be a compromise.
In contrast if I'd wanted to make it a DOS system, I'd have kept RAM as low as possible (32MB PC100), gone for CF-IDE adapter instead of SATA SSD, made sure to choose a PCI NIC with good DOS packet driver support, added a nice ISA sound card, preferably with wavetable synth and/or bug-free MIDI. And if I'd been able to run a Via C3 (which can be slowed down to almost XT speeds) I'd have used that and otherwise gone for a much slower CPU. For late DOS I find a P3-600 is around the sweet spot, but if I want to run earlier stuff (and a C3 is not an option) I'd want the lowest multiplier I could get - so a P2-350 would be best on a board without multiplier jumpers, then drop FSB in software. That's a very different system to the Win98 system based on the same board.
So: focus!
Your motherboard lacks those two advantages (good onboard VGA and an ISA slot) so you're even more limited. You still face the dilemma that Win98SE games will benefit from every extra bit of speed you can eke out of the system, whereas every bit of speed you gain will increase the number of DOS games that will have problems. I'd say ditch DOS on this system, go for the fastest PCI VGA you can find (good suggestions have already been given, but even a GeForce2MX PCI or FX5200 PCI would be a big upgrade if an FX5600 PCI is unobtainium), add a nice 3D sound card (Aureal 2 or SBLive/Audigy) and a NIC and you're good to go with Win98 games far beyond anything that would originally have run on it (and indeed beyond what I can run on my system as Voodoo3 beats Intel GMA, but is much slower than any GeForce, even on PCI). Oh, and you still have a PCI slot left. If you have more money than sense (or some very good luck), stick in a Voodoo2 for GLide. Or more niche (and if you like Tomb Raider), go for a PowerVR PCX2. I'd try to keep the exterior as original as possible so as to make the surprise as big as possible 😉