For affordable the Fobes Debut remain the most affordable option that are better than the stock mouthpieces. I personally have grown to prefer the Vandoren M13 Lyres for MS students, and M30 for my HS students if you can afford them. (They're not that much more in the grand scheme)

For ligatures in a school I will always say Rovner classics. Are there some ligatures that might respond better? Yes. Are there ligatures that can be stepped on and still work? They're one of the only ones I know of. They sound more than adequate enough and are nearly indestructible.