I don't use emails as placeholders for my actions. I want my actions to be in a list where I can easily see, in a single line, what each action is. There may be support material with more details, but when I'm deciding which action to work on, I don't want to have to see extraneous stuff. It can take a couple of minutes to open an email, read through it, and remember what action I thought it triggered; to me, that's an unacceptable amount of delay when scanning my action lists.
So I put the actions triggered by emails into Omnifocus, sometimes with an atttached note telling me which email (From and Date or Subject and Date) I might want to search for when I start working on the task. Then I put the email in one massive archive with all the other emails for that year. I normally do not sort email - on the rare occasions when I do, the sorting usually just consists of a temporary folder that I may use for a few weeks because I'm referencing a specific set of emails extremely frequently as I work on a project. After that phase of the project is over, the email gets dumped back in the archive.
This means that if I _had_ to use my email client to sort my actions, I'd re-mail each relevant email to myself, changing the subject line to an action description. If a single email produced four actions, I'd forward it to myself four times, each with a different action as the subject line. I'd probably have an email folder for each project, plus one for Someday/Maybe.
This may or may not be the least bit relevant to your question.
Oh, yeah - when to go through the inbox. When I'm working my system properly, I get my inbox to empty, all emails converted to actions (if appropriate) and moved to my archive, two to three times a day - first thing in the morning, after lunch, and I may or may not do it again before I leave for the day.
When I'm working my system sloppily, a few dozen emails may pile up, but I _always_ maintain the rule that emails not yet fully processed are either (1) left in "unread" status, even if I have to reset them that way after I read them, or (2) moved to my "when I can breathe" folder so that I know that immediate processing isn't urgent. Any "read" emails in my inbox can be moved to the archive without further review.
One more edit: I don't use the two-minute rule when processing emails. When I'm processing my email inbox, any and all actions trigged by emails are entered in my OmniFocus system. Moving something from the email inbox to the OmniFocus inbox only takes a few seconds; immediately performing two-minute actions distracts me too much.
Gardener