Where to buy
I bought the markers at Blicks. For the mugs I checked Goodwill first but most had a logo. I bought these at Dollar Tree. The boxes are photo archive containers from Target, they were the perfect depth.
Check the pens
My black + aqua markers worked great. I bought a 3rd color and after multiple returns tried markers in store with the manager. I ended up with gold porcelain paint-it was thicker but great as an accent color.
I was too impatient to trace anything first, but I drew quick pen sketches on the kid's construction paper. It was helpful in deciding which design would translate to the mug.
Wipe off the mistakes
If you make a mistake its easy to wipe off with a damp cloth. If its been a few days rub it off with some warm soapy water. It won't be permanent until you bake the mugs.