|You don't have to limit yourself. NT 4.0 will install on any modern machine, just get one that has PCI slots and ISA if required for video/sound/network.|
If you're going to be employing legacy ISA video/sound/network cards (the old long black slots), IEI Technologies still manufactures modern motherboards with 2 ISA slots on them (see here). The specific boards with ISA slots are the IMBA-G412ISA and the IMBA-9454ISA.
If you're worried about device drivers, it isn't hard to take NT 4.0-compatible video/sound/network cards from one old NT machine and put them in the newer one. As LMiller7 said, you won't find new video/sound/network hardware with NT drivers, so this will be your only route to get NT working with new hardware. To avoid messing around too much you're going to want a board that supports IDE drives (SATA can be done but may be challenging), and slots for PCI and ISA cards (ISA only if needed for video, sound, and network). Get a modern board and processor with 4GB RAM and NT will run very nicely on it.
I've installed Windows 95 and NT 4.0 both on modern equipment. Again, device drivers would be your only issue but I mentioned how to get around that. It's true hard drives don't last forever, but I've got video/sound/network cards from 20 years ago that still work. Cards have a lack of moving parts likely means a very long (but still finite) lifetime. There is no reason you shouldn't be able to get NT up and running on a newer board/processor/RAM.
If you need further guidance, let me know. Generally if you want it, it can be done.