Even if you wouldn't have a message like that (wait for 60 minutes), you have to understand that Exchange Online is a huge environment, in which replication of settings may not be done instantly. Because of this, even if you are not informed that you have to wait, as a best practice my advice will be to wait.
Related to the question about which Hold option should be recommended (legacy from Exchange Online, or new ones from Security & Compliance), indeed, Microsoft recommends the new ones. Even so, it is up to you (until the time you'll be forced to use just the new ones) which one is most suitable for you, when speaking about moving a mailbox into the Inactive state.