Help me stop using paper towels

This is something I've tried to stop in the past, but have always struggled with. I've never used them in the bathroom, but every attempt to replace them in the kitchen, or when cleaning up messes, has so far been unsuccessful.

I do now have reusable napkins for food, and that has worked, but cleaning up messes / plates is still a problem.

If I try to replace them with a tea towel or the like, I then feel like the tea towel is too contaminated to be used again. I also somehow manage to lose them quickly. Searching for how to switch over just leads to sites saying "use tea towels!" so I'd like to hear how those who have successfully stopped using paper towels have managed it.

[Edit-- I'm pleasantly surprised by all the suggestions, thank you! I'll look into trying the different options and making an individual laundry basket for them!]