As far as what type of hay- if you can get access to it, rotate it. One is never perfect. I simply get what is local- less cost that way. They are goats, they don't have the fussy digestive systems like horses do. You can rotate or just take whatever your local supplier has. I used to live in Port Deposit, MD- but didn't have goats then so I dont know what is local. Goats are not fussy, especially if you have either a goat block or free minerals.
As far as breaking them from the feed- same as breaking a baby from a bottle- messy, but somebody has to do it. They will quit crying after a few days when they get the hint. Only way I know of to do it.
Another thing- (sorry, love my goat babies) do not, do not, do NOT cut branches off trees and feed to them- there are some trees that are fine if the goats eat of them, and become toxic when they are cut. Please check your trees for toxicity before you give them to the goat. If a goat grazes something and gets sick, it will not graze it again. If you cut limbs they will eat them, and if it is toxic they may not realize the connection.
Goats generally eat from top to bottom and outside in. They will graze grass, but only if there is nothing else to sidetrack them. As long as you are giving them feed they probably won't graze the grass. But they will when that have to. So, give them a bit of feed, free choice hay, supplement with a block (I get my goat block at
tractor supply- if I remember, there used to be, like 20 years ago, a feed store in rising sun) or minerals, plenty of water and let them graze.