This little quote from the AIM is the source of a lot of confusion for new pilots.
In 4-2-3 (c), the AIM also says:
c. Subsequent Contacts and Responses to Callup from a Ground Facility.
You should acknowledge all callups or clearances unless the controller
or FSS specialist advises otherwise.
Acknowledge with your aircraft identification, either at the beginning
or at the end of your transmission, and one of the words "Wilco,"
"Roger," "Affirmative," "Negative," or other appropriate remarks;
e.g., "PIPER TWO ONE FOUR LIMA, ROGER."
Let me make it simple:
- You should read back those items that the AIM 4-4-7 specifies (and that you quoted in your question). Basically any time that they give you a clearance or anything that contains a number.
- You should acknowledge with at the bare minimum your aircraft call sign and preferably something that lets them know that you got their instructions/message and understand it, every time that ATC talks to you.
- The one exception is after you have been handed off to the final controller on a PAR approach, you do not acknowledge their instructions. They come too fast and you will have your hands full (and they specifically tell you this after your initial contact.)
As a short aside, you should know that there is case law which says that even when a pilot reads back a clearance incorrectly, the controller is not legally obligated to listen or correct the pilot. They consider it the pilot responsibility to hear and understand all clearances. For instance:
Controller: Cessna 1234, descend and maintain 3,000 feet
Pilot: Cessna 1234, Roger, descend and maintain 2,000 feet
Controller: No response
Pilot: Descends to 2,000 feet because that is what he understood, and
may now be violated for it.
That being said, most controllers are very good and catch mistakes like this that you may make, but I have heard conversations in the cockpit along the lines of "it must be right because they didn't correct me when I read it back" and this is a situation ripe for problems/violations. If there is ever a doubt, ask for clarification!