If you have a hamburger at a fancy deli they'll often have a very fancy bun. However, I have never seen these buns for sale at bakeries or grocery stores.  What kind of different buns exist for "high end" (15$) hamburgers? I'd like to get a list of as many of them as possible and then I'll narrow my search to the ones I can reasonably make or buy. 
It won't be viable to leaven bread. Too soon and you'll just be using it in the leuconostoc stage which is bad bacteria and isn't good for anything. I wouldn't use the starter or discard till it becomes viable.  