While I easily use an overclocked Pentium III Tualatin-S as my main system since a year, I don't know how much of usable a 486 system can be nowadays... But here are my two cents. You'll need to squeeze every bit of performance you can out of that computer. So, instead of a 486DX4-100, I'd rather go for a 5x86 system, either AMD or Cyrix (although I'd prefer the former, as I don't know how much you could cope with the weak FPU of the Cyrix 5x86). Also, a PCI 486 motherboard is a must, because you need something that can offload the CPU as much as possible when it comes to the basic I/O operations, and so you'll need a PCI hard drive controller, either SCSI (U320 would be preferrable), SATA (you could use an SSD on your 486!) or ATA133, it would let you use a modern hard drive/SSD and bypass the BIOS limitations, as long as it lets you boot from SCSI.
Second thing, the graphics card. If it's a PCI 486 system, you'll have to find the fastest compatible PCI graphics card you can put in the system. Considering that there's no AGP slot for it (I wish!), you'll have to pick something that could be compatible with the CPU, as I don't know if the latest PCI graphics card support the 486 at all or need Pentium instructions. Maybe a PCI Voodoo 3 could do the job? Either that or just anything high end made for the PCI bus, as long as it's not an S3 Virge or a Trident.
Another thing, the OS. Yeah, you can go with Linux, but if you have enough memory, you could even go with Windows 2000. A Japanese developer, Blackwingcat, made a kernel extension for it that lets you run most of the Windows XP only applications on 2000, and it runs -I tested it on my Tualatin, but it wouldn't run the programs I needed so I reverted to XP- and doesn't consume that much of RAM. If you can, don't forget to tighten the RAM timings as much as you could, to gain a bit of extra speed. Other than that, if I manage to cruise along with a Tualatin-S, a CPU that was faster than the early Pentium IVs, you could maybe achieve a similar result with a way older CPU than mine.
In the end, a little tip about the Pentium II: put it in a BX board (or even better, a Slot 1 VIA Apollo Pro 133A one), put some PC100 CL2 sticks (PC133 in case of the VIA one), run it at CAS2, use a PCI SATA controller with either an SSD or a WD Velociraptor and put the fastest AGP card you can find (being the old 3,3v AGP slot your choices are limited, so I'd pick a Radeon 9800 Pro, just because the nVidia Geforce FX series is terrible, performance wise), install Windows XP, slim it down of all the unnecessary services and crap running in background, install Mozilla Firefox 47 (which runs on a Pentium II!) with the UOC Patch, and you'll enjoy a much faster Pentium II system than you thought it would be.
My Retro Daily Driver: Pentium !!!-S 1.7GHz | 3GB PC166 ECC SDRAM | Geforce 6800 Ultra 256MB | 128GB Lite-On SSD + 500GB WD Blue SSD | ESS Allegro PCI | Windows XP Professional SP3