It really just depends... if I am looking for a stacked bowl with a really narrow chamber and for pot shapes with wide chambers, I don't mind a more narrow draft. For a 5" to 6" long pipe with a midland .75" to .85" wide chamber, I like a more open draft. I like variety in sizes and draws.
The button is important too, but if I am looking through some factory pipes, it's not a deal breaker.
I would prefer vulcanite, especially brindled, but if the button is nicely done, I'd consider acrylic.
If it is going to be blasted, I want deep craggy blasts, not one that looks like the blast was just quickly done quickly without much thought on an assembly line.
It just has to speak to me. I don't buy many pipes online, because I'd rather hold it and pick up some of the nuances of the pipe. And, I am lucky to have one of the best pipe shops in the US just down the road.
When I have purchased a pipe online, I am usually surprised by some of the differences between seeing pictures of the pipe online and having it in hand. Not, that the pipe wasn't as pictured, but that I just don't notice or get a sense of the pipe's scale and overall-ness.