We all live in different parts of the world so the "best kind of hay" is different for all of us. Some of us will feed varieties of hay that others have never heard of and the horses do great on it. What is your best kind of hay is first grown locally, is affordable, is put up right, is appropriate for the classes of horses it is being fed to, keeps your horses in good condition and your horses eat it and waste little. Looks aren't everything either. The south grows some types of grasses that don't look like a steer would eat them but they are good horse forage. If you think your hay looks inferior in quality, the only way to know for sure is to have it tested. That's a good place to start and it's good information to have for creating an overall dietary plan. It's cheap as well. ($20-30)
Feeding round bales invites a lot of waste. The horses will dig through the bale looking for the tasty bits and throw the stuff out they don't want right now. Place the bale in a round bale feeder, place a slow net (can be as simple as an old soccer or hockey goal net or snow fence) or put the bale outside the pen up against the fence where they can still reach it. Most horses don't like to splash their legs with urine and don't think twice about peeing in the hay.