eigenvector ; I'ld like to throw a couple of things into this mix, if you don't mind. Feel the top 1/4" or so of your cylinder. Do you feel "ANY" kind of a lip ? If so, you Absolutely Should buy/rent a "Ridge Reamer". This is a tool that when used will remove the ridge that forms at the top of a cylinder over time (don't know miles or internal condition of your motor). Since your installing New rings, they will have sharp edges on them. If you don't remove the lip around the top of the cylinder then you stand a Good chance of breaking at least your top ring (minimum) or worse, the ring land that is between the top 2 grooves (junking that piston). The tool isn't hard to use. Simply insert it in the cyl. and adjust out till slight contact is made with cyl. wall. Apply a little pressure on the wall and start turning the tool, adjusting to keep slight pressure till the lip has been removed (then stop). Then the next item you'll want is commonly ('round here anyway) called a "dingle berry hone". It looks like a cylindrical wire brush with balls of grit on the end of each one. This is the tool you'll use to put your "crosshatching" back in with.
I hate to disagree with "flybox" here but you don't want/need the 3-stone expanding type. Those are mainly used with Newly bored cylinders where the cutting/boring tool has taken out "Almost" all the material for New pistons (leaving Only a couple of thousands of material, then one would use the 3-stone hone to remove those last very few thousands. Then finishing it off with the "dingle-berry hone" for the crosshatching. "flybox" is correct on using lubricant, slow speed, oscillations and 45 degree crosshatching.
Hope I haven't confused or scared you in any way, LOL !
...cougar...