The small cup is Fine but of course small and harder to control the lather from rising out of but good enough where Ill keep it and use it for travel.
FWIW, I just use a leftover coffee cup, but sometimes I go online at eBay and look at all the old vintage shaving mugs, and maybe I'll buy one someday.
When travelling I don't take a mug with me, but I take the cake of shaving soap, and just drop it in the bottom of a drinking tumbler from the hotel. When I'm done, I just take the cake and leave the glass behind. At least it means they have to wash it !
I have no idea what works best, but I like to drop the brush in the bottom of the sink and run hot water over it for about a minute while I'm doing something else. Then pick it up, shake off some of the water, and use what's left to churn up the lather. The lather tends to be warmish that way. A brush with a bit of water on it makes a good lather, too much is too runny, and a dry brush won't churn up any lather at all. Try things, make mistakes - its only shaving.