it's easier than you think
we've been paper towel and napkin free for about 4 years. my husband wears undershirts and goes through them pretty quickly, so we cut the old ones up for rags. we also cut up any old cotton clothing (socks, shirts, etc) as long as they aren't too worn out. i keep the rags near the cleaning supplies (also conveniently located off my kitchen with the laundry) and we use rags only for the pretty gross stuff- cleaning up meat juice spills, the bathroom, pet accidents/barf, etc. Then for the "cleaner" messes such as dishes, my baby's face, the counter, etc, we use dish towels and wash cloths.occasionally a mess will be so nasty that we just throw out the cloth rag.
i toss any solids away in the trash from the mess (of course) and throw the rags in a plastic container on top of my dryer. towels, wash cloths and cloth napkins go in a separate laundry basket in the same location. i do laundry about 2x/week.
and yes, you will get looks.
my brother in frustration once yelled "i hate that you don't have paper towels!!" no matter, i find the cloth to be a lot more effective on messes.






Now if I could just get DH to take the family cloth plunge 




Anyway, we just lay bacon on the paper napkins. I also use the napkins on any really scary messes, like dog barf.
but I do occasionally need something to pick up grease (when I'm cleaning the cast iron skillet, which I almost never use water on) and for that I use old cut up t-shirts rags. I cut them into about 5"x5" squares. When they're dirty I throw them in with the dish water (I wash dishes by hand) to let the grease dissipate before putting them in the washer.