Versailles can take most of a day. The drive to Amboise isn't too bad but expect to be fairly tired when you arrive.
Advance tickets aren't mandatory. If it's a nice day in early September, however, it's probably optimal to arrive at Versailles with pre-purchased tickets at least 30 minutes before opening. You will have to go through security, so leaving any large bags in the trunk of the car will save you having to check and recover your bag (I had to check a full size umbrella, but a fold up one would have been okay).
We went straight to the main thing, the mirrored hall, then the garden and petite palaces, then decided we were too worn out to go back for more of the main palace.
The Loire Chateaux are different. I never saw a big line at even the most popular of the Chateaux. Purchase your ticket when you arrive and you will be fine. No need to arrive early either. There will be plenty of people but they drift in and out all day.
In one day (with a rental car) from Amboise, you can probably see Chenonceau, Amboise and Clos Luce. I did it with a bicycle. The only problem I had was missing most of the gardens at Clos Luce because there were more than I had time for. I think you should visit Chenonceau, it seems to be everyone's favorite (including mine).
The one thing I'd do in advance is use Google maps and click on each place you are interested in. The left part of the screen (scroll down) will have the current open hours. Make sure you know the hours, opening, closing and what day they are closed, before you start out.