I bought a hugh pack of dishtowels at bj's warehouse about 4 years ago and I use those all the time to wipe up spilled juice or water. I use small dishrags (again a hugh pack bought there) for wiping down the counters, table and smaller messes. I use homemade cloth wipes and washclothes for kids hands, faces and the baby's bum
. As for napkins I made some myself, but I'm thinking of buying a few too just for variety.
The wipes go straight in the diaper pail, the towels and cleaning rags get hung over the sink or the top of the washer (I leave the lid up to hang stuff on) until they are dry enough to toss in the hamper. Then after a few days I do a towel/rag wash load.
Walmart, target, sam's, costco all those places sell large packs of 'bar cloths' dishrags etc each store seems to call them something different but they all work great. If you get all white ones you could bleach them to get out germs. I just use a really hot wash and an extra rinse.
I still use paper towels to clean up meat spills in the fridge or to wipe down the counter after breaking down bigger packs of meat, I'm just not comfy with that kind of mess on a towel. Since that's all I use paper towels for they last forever.