I'd go for a socket 370 platform. 440bx slot 1 motherboards are more expensive then a late socket 370 boards witch can be had for as little as 10$ second hand or 45$ new . New means stability, and that seems to be what you're most interested in. Here's a link: https://www.alibaba.com/product-detail/VIA-69 … .220b4534VcRUz6 The seller also claims that is supports Tualatin chips, and Ithere are a couple of youtube videos of this board. In one it's even running a 1400MHz tualatin celeron.
Better yet, if you can score a VIA C3 CPU (the faster the better) you will be able to run anything from 80's dos games to late win98 games, since the VIA C3's multiplier and cache can be changed while the computer is running using setmul.
They're not expensive either - a 866MHz C3 can be had for 20$, while 35$ should get you a 1200MHz version. I recommend the latter because the C3's floating point performance is weak, so a 1200MHz chip should perform on par with a 600-700MHz pentium 3. https://www.ebay.com/b/VIA-Computer-Processor … /164/bn_2794436
It's like heaving a 386, 486, pentium and pentium III all in one machine.
So a brand new mainboard for 45$, 1200MHz VIA C3 for 35$, 256MB of new old stock PC133 SDRAM ~ 12 to 15$. A 440bx rig will get you well over that - a decent mainboard alone (second hand) is 80-120$. Slot 1 CPUs are cheap - at least most pentium II's are, but if you want a later 800+ mhz slot 1 pentium 3, be prepared to shell out some serious cash since you'd need the 100MHz front side bus version, as the 440BX does not support FSB 133.
As for a video card - it shouldn't really matter. I'd say try to get a hold of a voodoo 3 simply because it has glide support as well as great dos games compatibility - but they are expensive... a geforce FX 5500 as mentioned above will work fine, and you can find a NEW FX 5500 AGP for 25-30$ on alibaba.
Good luck with your build!