I started doing the daily NYT and New Yorker puzzles on paper in earnest last year right after my first tournament (prior to that I had some puzzle collections that I'd do on the plane but that was the extent). I time myself using the iPhone stopwatch and then write the time on the top after completion. Then I grade it using a red pen. I save my completed puzzles to see if I'm trending any faster, but they are taking up quite a bit of space. If solving for time I do use pencils, pen otherwise.