My husband usually golfs solo so he has to wait until closer to the date he wants to golf to be fit into a time slot (at least I think that is what he said), so I'm not sure about timing for reservations with more than 1 person.
He usually takes the complimentary taxi from the Disney resort to the course and then back. He usually has the bell staff or front desk take care of it and they call the taxi and then give my husband a voucher to give the taxi driver. I never asked him but I'm sure the process is quite similar at the actual course.
It's been awhile for him golfing Palm but he likes Magnolia and Lake Buena Vista a lot. He likes to shop at the clubhouse a lot too because he often wears the golfing polos when he isn't golfing. I think Oak Trail is his least favorite but even then he likes it.
He usually brings his own golfing shoes but rents clubs at the course. He says the rental clubs are much better than his own at home so he feels more like a pro at Disney!
If you have some specific questions I can ask him for you.