What are the new rings made out of? Steel, cast iron, chrome? Don't use a bar hone unless you've done this before, and successfully. Get a ball end hone that is about 10-20% larger than the diameter of the cynlinder. Duct tape up the other holes in the block, both oil and coolant holes, because this is a messy job. I would also throw a wrap of tape around the crank journals to seal off the oil passages there also.
Use a good oil, dip the entire hone in oil, you want to have the hone always spinning, though very slowly when ever it is in the cylinder. You don't want ANY verticle scratches, just diagonal criss-crosses. I'd use a 160 grit hone. Probably no more than 3 in and out passes, 4 at the most, and of course always moving, never stop the hone on the inside because that will leave verticle scratches when you pull out the hone.
After you've done all six holes, soak a light colored rag in ATF and wipe down the cylinders until the rags no longer show dark iron grit. Keep wiping. I don't like to hone anything that can't be cleaned thoroughly. A gallon of mineral spirits sprayed up inside the block will help float a lot of that crap off of the rough castings of the block so that you oil doesn't do it later.
I would definitely do a couple of short oil changes when you get it back together, if you don't have a way of thoroughly cleaning that block after honing.
Good luck.
Tom