What is the best method of personalizing a mug? (See details)

Basically for Christmas I have drawn something specifically that I want to put on a mug for a gift for my bf. I assumed the best route would be to draw it, scan it into the computer, and send it to an online store and have them then ship it to me. If that’s the case, what is the best, highest quality web site for doing so with the most options for mug styles, colors, etc? If there is another way to do it, I’d like to hear about that too. I don’t want it to look cheap or fake or like it’s “transferred” onto the mug. It’s kind of a big deal, we both have this weird thing for coffee mugs lol. I was thinking maybe there is some type of thing where I just draw ON the mug and then put some type of protective coating on it? Um, am I crazy? Basically I’m just looking for suggestions or anything that comes to mind for something like this, as I’ve never really done it before. Also it’s going to be very colorful, if that matters. Thanks fine folks.