[Anguirel]

You answer some of your own questions. The Three are not of Sauron's making, and so would not "wraithify" (it's a word now!) the bearer.

I expect the Nine and Seven (which are made with Sauron's aid and are a different case) would look aesthetically different from each other, and perhaps have different floklore surrounding their properties and origins. However, the sets of the Seven and Nine would not differ from each other apart from the general differences between each ring. As Estelyn rightly points out, they all come under the many rings crafted by Elves (insert "and Annatar".)