Only thing I would add is that I used a very, small, pointy, heavy pick; Dunlop Jazz III (yep, Chris, I strum a Jazz III). So, for me, it isn't the pick thickness but how you strum. Chris' tutorial explains it well. My only add is that when your strum or pick, you don't need to kill the strings. You just have to strike them. Many players don't use a pick and obviously, the aren't beating their fingers to death. Strums should be a natural extension of what you would otherwise do with your bare thumb if you were strumming or picking a string without a pick. Try it a little without the pick to see what you would do just with your thumb and then try picking a pick again with the same motions.

Food for thought.