Getting the right seat post
Usually at the "Cut out" in the top of the seat tube, they measure a little bigger than the actual size of the post. I'd say your best bet is to try several sizes at your Local Bike Shop, there even used to be a tool to measure it, but it's rather hard to find these days.  If I had to guess, it's probably a 27.0 or 26.8 just judging by your measurement.