PII is still old enough to work with DOS, since they usually still have ISA ports. But you might run into some problems with games that depend on CPU speed for timing. That manifests in either the game running too fast, or problems with audio, crashing, etc.
IMO, if you want a good span, keep a Pentium and a Pentium III, and something modern. If you have, say, a Pentium 166 and a PIII 850, that's good for a huge span of games. You will still run into some oooold DOS games that don't work right on a Pentium, but for those you pretty much need exactly the machine it was meant to run on (like a 4.77MHz 8088 or a 286).
The one advantage of having the PII and PIII is a little bit of diversity with the graphics cards. E.g., maybe you want to use a Voodoo for GL in the PII, and just a run of the mill Direct-X card for the PIII. I use a Matrox Mystique (because I love the textured special edition of Mech Warrior II it came with) in my Pentium with Win 95. My PII with Win 98 has a Voodoo 5, and my PIII with Win ME has a Radeon 8500. Overkill for the average retro gamer, but I just like the hardware.
For sound, you probably want an ISA SB16 for DOS, unless you have something specific in mind. For Win 98, a Sound Blaster Live! is good -- it'll get you EAX, which can be fun -- but really it's a lot less critical once you're in Windows and have driver abstraction.