Using excellent condition Starrett telescoping gauges and a good micrometer I still find it challenging to get accurate and repeatable piston and bore measurements. It is possible but challenging. A good quality cylinder bore gauge is the tool to use and still takes skill.
I assume that when you say calipers, you are referring to something like this:
With those, I do not believe there is any hope of achieving a measurement accurate enough to be useful (despite the accuracy the manufacturer might claim). 20ish years ago, before I had decent tools, I tried using digital calipers to measure engine internals and the measurements were not accurate enough to be useful. Thankfully I had a friend who had decent measuring tools and was kind enough to assist me.
If you aren't in a position to get (at minimum) a decent micrometer for the distance you are measuring, then take it to a machine shop and pay them to measure it up. That will actually save you time and money in the long run.
You also can't get useful piston measurements with the pistons installed. Measuring the diameter of the piston crown as it protrudes from the block is not useful in determining piston wear.
Yes, the skirts are larger diameter than the crown and the skirt is what you need to measure.