Fred,
My priorities are:

1) Do I want to wear this bead? Many beads are very beautiful, but I don't see myself wearing them. That is a complex thing to try and explain - partly it is a matter of my own taste for certain colors and designs- but sometimes I can't explain why some nice beads are just wrong for me. I'm not sure that is exactly "connoisseurship".

I should also add that often it is very challenging to figure out exactly how to wear the beads, once purchased. I have to look very long and hard for matching or coordinating beads, and also accept a good amount of non-uniformity in the finished product.

2) Provenance - I've decided to specialize (nearly always) in Venetian and Bohemian trade beads so I am concerned about verifying that the beads are authentic. But, reason #1 ends up being the deciding factor if I'm not sure. I have a small collection of trade beads that have no immediate plans for a wearable design, but this represents a very small fraction of my collection.

But your question is very thought-provoking!