Before proposing reviewers, should I notify them? Some journals require the author to propose potential reviewers. Should I just propose reviewers and let the editor contact them? Or should I first contact the potential reviewers myself and ask if they agree?
I never asked them and never heard of anybody doing so. It’s the journal who is responsible to organise peer review, not you, and they have to and will humbly ask¹ potential reviewers anyway. By asking potential reviewers yourself, you cause the following problems:


Not every reviewer you suggest will be chosen by the editor. For a reviewer who will not be chosen to review, deciding upon your request will be a waste of time.
Even a reviewer who is eventually chosen will waste a little time by responding to the same request twice.
If a potential reviewer declines your request and you do not suggest them, the editor may still choose them on their own (most editors to whom I have talked make a point of choosing at least one reviewer who was not suggested). In that case, the potential reviewer may think that you ignored their wish.
Asking reviewers directly is a first step to breaching the independence of peer review as it opens up the path for manipulating peer review: “Sure I will review your paper [favourably] – provided that you will do the same thing for my next paper.” Some oppose even the mere option to suggest peer reviewers for this reason.
If you know only a limited list of potential reviewers for your paper, removing those who deny your request may make the list smaller than what is requested by the journal. If those reviewers only refuse when asked by the journal, you still did your duty of suggesting sufficiently many potential reviewers (and this may not even be a problem, if the journal requests a list that is longer than the number of actual reviewers).
You waste some of your time by asking the potential reviewers and waiting for their response may delay the actual submission.
If you show your paper to your potential reviewers privately, they have an advantage in the rare case that they try to steal your ideas or commit other dishonesties. By contrast, peer reviewers are often bound to terms of non-disclosure and similar and also the journal serves as an independent register of who had knowledge of the manuscript. This point does of course not apply, if you trust all potential reviewers or published a preprint of your paper anyway.




¹ Except perhaps for some journals with a questionably demanding demeanor.