You shouldn't have a problem booking anything at all.
I didn't start trying to book until about 2 weeks before. We are not planners.
I got everything, including mine train, without much of a problem. It was even easier once we got there. I got 2 more mine train (out of several options), and saw A&E several times. Even booked A&E once, but let it go because we really had no interest of seeing them.
Remember to have your whole day empty before attempting the headliners. When I did see mine train there were only a couple of choices of time, so if anything else had been in , or near, that time, it wouldn't have shown available for that day.
Many people are reporting seeing Mine Train and A&E reservations available only days before the desired date. I wouldn't worry much unless you have a larger group.
We were there 10 days (although you can only book 7 of those days) so we had a good amount of time to work with.
Never did see Be Our Guest available, but we waited on a 15-20 minute standby to eat there.
Good Luck, have fun!