This topic really went quickly!
I'd still suggest to find a Socket 370 board, but it doesn't necessarily have to be a Tualatin board imo.
Iirc there was someone selling already pinmodded Tualatins on Ebay that will work in most Coppermine boards. I'd suggest you get one of those.
If you're looking for a Socket 370 board, then I'd suggest you have a look here
This lists virtually all Socket 370 board along with their chipset.
If you don't want a Tualatin, then imo a fast Coppermine is good enough for a retro rig also (a 1GHz Coppermine is still very fluent with 98SE and I'd guess will be a lot cheaper. Heck, even an 800MHz variant will be quick enough!).
I'd somewhat advice against a Socket A system though as you'll first need to find a PSU that has lots of power on the 5v line (virtually all modern PSU don't have enough juice on the 5v line to power an Athlon or Athlon XP). The only exception to this rule are some of the very latest Socket A boards that came with the 4 pins P4 power plug, but most of them don't have this plug and thus draw power from the 5v line.
With a Pentium 3, this isn't really an issue since Pentium 3 (despite also eating from the 5v line) consumes so much less power than an Athlon or Athlon XP.
For graphics cards, if you go the Pentium 3 route, then the best would be a Voodoo 5, though those aren't very cheap these days. A second good option would be a Geforce 2 or Geforce 3 or so along with Voodoo 2 in SLI (which also isn't very cheap these days, but you could always use a single Voodoo 2 board). Another option would be a Geforce 4 or more recent (and more powerful) graphics card and use a glide wrapper, though I don't really know how effective these wrappers really are.
If you go the Pentium 4 or Athlon64 route, then this would be somewhat easier, as long as you stay with AGP.
I don't know what else to add now, many good tips have already been given 😀