I am a beginning band director and I'm trying to figure out the best mouthpiece make and size to start my students on. Any suggestions?

Sadly it isn't a one size fits all problem. What kind of school horns do your kids play? To start I would just have them use the mouthpiece that comes with the horn until they gain some level of proficiency. After that they should either work with their private horn teacher to pick a better mouthpiece or just start trying various models. The perfect mouthpiece for one student will be a disaster for another.

I retired in 2014 after 30 years as a middle school band director and now I am happily playing my horn again - a lot! I would recommend a Farkas MDC as a good all-around horn mouthpiece. It has a decent rim (not too thin) and the cup is not too shallow. Later, for more experienced players who can find their way around on the notes, I usually asked the parents to upgrade the mouthpiece to a Schilke 31C (1 or 2). That would be a mouthpiece that would last them through college.

I love mouthpiece.

I have been changing my opinions over the past few years, about mid and larger cup mouthpieces for beginners. Sure they make a great sound, but I prefer that the students gain a modicum of comfort with notes before attempting to find the perfect one (which I spent years trying to do for myself). I just let two of my beginning students try my newly acquired Maelstrom MS 4.4 It is tiny by modern American playing standards. These two immediately had better articulation, accuracy, and intonation. In the 15 minutes they played on it, the change was radical. I tried the same experiment last year using a Laskey 75G I retired when I found I was still reacting to it, even though it is purportedly hypoallergenic. Last years Band Booster scholarship kids all did much better on that than the larger school mouthpieces. I also recommend that everyone use stainless steel with either a stainless rim or synthetic of some sort. I've run into a lot of kids that you can tell are having a reaction to the mouthpiece they are using.