IMHO, unless you've got really sensitive, perfect pitch type ears, I doubt you'll hear much if any difference between Delrin and horn, bone or wood for the nut & bridge. There really is no "ultimate nut and bridge material", it's personal preference. I personally dislike bone/horn because it stinks when you're working it. Metal vs a softer material does make a sound difference. I like various hard woods or pieces of thick-walled bamboo for nuts & bridges.
Wood choice is also very personal. You'll get people who will tell you 'this wood sounds better than that' yada, yada. There are hundreds of factors which go into the 'sound' of a dulcimer, and wood is fairly far down the list, actually. A decent luthier can tweak any woods to make an instrument that sounds the way you want.
When you're ready to jump into building, join the Dulcimer Building Group here, read a bunch of out posts, and ask your questions. We've talked a number of new builders through their first or fifth build.