Sketches should be visceral, messy, and fast. The entire purpose of sketching is to get the ideas out as quickly as possible.
I don't understand the purpose of creating preliminary sketches that you then redraw on nice paper. Are you trying to design a UI or make a pretty picture?
Also, throw sketches away? Are you crazy? Keep them. Later when you are adding a feature or changing the UI, you'll be glad to have those ideas to return to.
I use whatever pen is sitting around (usually the cheapest money can buy), and whatever paper is handy (usually scrap printer paper with stuff on the other side). My sketches are ugly and I take no pride in them.
The widget shown in the post isn't that great of an example. I'd have no idea how to use a UI like that in a real context. Also, it seems like you just chose to build the very first thing you sketched. You say design is iterative, so where are all the other concepts?
Sorry to be so brutal. I appreciate the spirit of your post. I agree with your rationale for sketching, but your examples/practices don't seem to match it.
Throwaway sketches and thumbnailing are a hack for dealing with creative block. It's a pretty well-known technique.
It's definitely not meant to be prescriptive, and I hope not presented as such. What works for me might not work for you. Bonne chance.