If I'm reading your question correctly, you're looking for an affordable build for Win 3.1, not the "ultimate"/fastest one.
Pentium I is definitely an option. Consider that before Microsoft released Win95, you could already buy Pentiums with speeds up to 133 MHz, so if you had an early Socket 5/7 system, Win 3.11/WinNT 3 were the way to go for a while. I've used it on a system running Pentium 133 on an Intel Thor motherboard with built-in S3 Trio64 videocard, a Crystal audio chip and a 3COM ethernet card. I had no issues finding the drivers.
I vaguely remember installing it on a Pentium 4 system 20 years ago as a kid (just for fun). While I imagine that I wouldn't be able to find any drivers, CPU speed is probably not a big issue for Win 3.11.
All in all, I think your biggest issue will be finding drivers for your expansion cards. I would just pick any S3 Trio/Virge, a 3COM Etherlink for network and any SoundBlaster clone. I can't think of any ISA sound card that doesn't have drivers for Win 3.11, but a quick google for a chip model + "Windows 3.11 drivers" will help you make a decision. All of these parts are usually cheap and easy to find
One issue I remember is that by default Windows 3.11 has 32-bit disk access disabled. If you'll enable it you won't be able to use disks larger than 524MB. To fix that you'll need drivers for your disk controller, and this is where you might have problems. However, without drivers the system will still work, just slower.
Pentium 166 MMX Overdrive, 32 MB RAM, Ark Logic ARK1000VL, Tekram DC-680C, Turtle Beach Tropez, Gravis Ultrasound Max
Pentium III 1000, 256 MB RAM, Matrox G400 MAX, Adaptec 19160, Yamaha YMF740B