1. For the purposes of the exhibition I would define as 'rare' something that has major design aspects that are different from all (or most) of its peers. Not just a different twist on the borders or a gul with a different interior. "This is the only known Salor three-gul-chuval with no silk in the pile' doesn't qualify.
2. As far as beauty is concerned, it IS in the eyes of the beholder. If you have a committee, I would give each member a free rein to choose some pieces purely on his or her taste. For the rest, I'd look for a consensus among all or most of the committee members.
3. I would prefer a wide coverage of different areas over a choice by purely esthetic criteria.
4. This is the American conference on ORIENTAL RUGS. Nothing else please - not because I don't like to see other textiles, it's just that would make it too open-ended.
5. Synthetic dyes? you'd open a can of worms trying to prove that there is not a single knot with synthetic dyes. Besides, if you think a rug is beautiful, you shouldn't care. If you cannot think of a rug with synthetic dyes as beautiful, then you wouldn't have chosen it in the first place.
6. I'd skip new rugs for now, but perhaps it wood be nice to have a separate exhibition dedicated to new rugs at some venue soon. But if a committee member exercises his or her right to pick a new rug (see question 2), then who can argue?
7. Fragments and tattered shreds should be included if they are visually pleasing or historically significant.

Regards, Yon