Bits and pieces...
The Mitutoyo verniers I have in the garage are rated at 0.02mm, well inside what you need to do. Most manual verniers should be able to easily beat 0.1mm.
Smaller vernier calipers may have jaws too short to reach around the piston properly. Although a 125 piston is probably small enough that a standard 150mm vernier should be OK.
If using digital calipers,wipe the jaws first, zero, take your measurement, re-check your zero afterwards.
There will be a correct way and place to measure the piston diameter - see if you can find a workshop manual with a picture of this.
There is a tool known as a telescopic gauge, you put this into the bore, lock the gauge, then remove it and measure the gauge with an external vernier or micrometer. Here's a set:
http://tradetools.co.nz/products/4830320
They require patience and skill to use but are far cheaper than dedicated bore gauges. Errors in angle / centering will affect the measuement.
If buying measuring gear, Insize is good, Mitutoyo is very good. You won't find either of these at the local hardware shop, go looking at dedicated engineering shops. The cheaper brands like Kingchrome... Nope. Their manual stuff is OK but the battery powered digitals suffer track errors and eat batteries.
The gear's expensive. I spent around a hundy on the 150mm manual Mitutoyo calipers... it seemed horribly expensive at the time, they're now one of my most important workshop tools and I couldn't imagine doing engine work without them.
Finally... the advice about skipping all this and finding a friendly engineering shop or engine reconditioner's is spot on, turn up with piston and barrel neatly wrapped and cleaned (this will go a long way) and they should sort you out in less than ten minutes.
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