Do you treat your pencil to hand sharpening, or just use a commodity sharpening tool? 
I recently came across this site that let you print your own dotted paper which is a nice compromise.
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.
Its just much more fluid for me to spill out my mind onto paper than diagrams or UI layouts on the computer.
I'm sure one day when you can draw onto a tablet just like putting pencil to paper I will switch, but that day is a long way off.
A Cintiq is 5% the way there. And digital pens for tablets are as far away as a mouse.
Any lag, any lack or precision and also the back light are all issues. I am confident they will one day be solved and I will carry a true digital notebook where the contact of pen to paper is indistinguishable from the real thing.
Why do I long for this future? Because I love digital and I wouldn't all my work on paper being stored as a digital notepad. (Scanning is not a solution because I want to pull up notebooks from the past and work on them using my "digital notebook")
This was a bit a pointless post actually, Instead of deleting it I'll leave it here in-case anyone has anything to add or disagree with.
Before settling on a tablet, I considered the Wacom Inkling and even tried using the iPad and a few apps, but could never quite get the same level of precision as I can manage with a pencil. The tablet's just a stop gap, and keeps me from going crazy and loading up a boatload of sketching gear (psst… Copic pens). My Intuos 5 + Autodesk Sketchbook Pro combination gives me some degree of freedom without the clutter of gear I'd unavoidably end up with if I went shopping for stationery.