sky, your mileage may vary, but when we were going a bunch, we weren't too picky about type. What we wanted was quality, not a bunch weeds, sprouts, bs in the hay. And we didn't want to change once we got started on a type of hay. We usually bought several bales once we found a good supplier that was reasonable around home. If we were on a trip long enough that we would run out, then we did the best we could. My favorite hay was timothy/orchard grass, and bermuda. But, we had to be careful with really good bermuda as I had a horse colic on it before. Stems/leaf was really fine, and he wasn't drinking enough water to move it. He was a slow starter on drinking road water, he'd hold out a day or two, then give in and drink strange water. We didn't have an onboard tank at the time.
I love the smell of alfalfa and it's a good hay, but too much protein for what we needed and was harder on kidneys I was always told. Clover, if cut right, is hay I liked, but seeds would make them slobber, and have heard of mouth infections due to them before. Idk if that is true though.