Bowl for me. Ceramic is preferred. I buy them cheap at WallyWorld. If I drop it, which hasn't happened, they're cheap to replace, and the ceramic holds enough heat that I can fill it with warm water, load my brush, and empty it and then make lather, and still have it be a bit warm. About 5" across is good for me. I use small brushes, so I don't have to worry about the "clank".
Mug for me. A mug takes up less space than a bowl. I wanted a mug with a brush holder built in, and no bowls that I know of have this feature.