A couple tips:
Place a rag or cover with blue masking tape, the case after the jug is removed BEFORE you remove the piston. Keep track of the circlips, you only have to remove one. Install one new circlip on the new piston before any other assembly.
Spray gasket remover works very well on carbon deposits. Just spray it on , when it's soaking, you can see all the splooge coming off. Finish up with a can of brake clean. You can use a toothbrush to help too.
On a few motors I've worked on, I was able to install the piston in the jug before placing it on the case. This eliminates trying to compress the ring(s) and holdong the jug at the same time. Just install the base gasket, line up the wrist pin, install the 2nd circlip and carefully push the jug on the case.
When the piston is off, very carefully pull up and down on the rod to check for play. Side to side is ok, just not up and down.
When fitting the piston to the jug, I give the cylinder and piston a very light coat of engine oil. This will help in with the initial break in. Also use motor oil on the wrist pin and bearing.
Be very careful not to gouge the case when removing the old gasket, if some pieces of gasket fall on the crank, use a vacuum.