1st year educator, played Euphonium as my major instrument through out undergrad. I have a Mack Brass Tuba on the way and I already know the default mouthpiece isn't going to cut it (I have a Mack Brass Euphonium, I don't even know what I did what that included mouhpeice the day I got it). I usually play on a Denis Wick Steven Mead Ultra 3 mouthpiece, which is pretty much the deepest cup that I could find. I love the mouthpiece. On trombone or my small bore Euphonium I use a Bach 5G, which I used in college for our marching horns and it's a decent mouthpiece. For cornet I use a Denis Wick 2.

So if you can't tell, I generally like deep cup mouthpieces. I don't want or need anything too fancy as I'm only using the mouthpiece for demonstration for my students and personal etude work. Any suggestions?