Keep your Inbox, Google
Unlike many people out there, I have no problem with email. It is a convenient way to communicate and maintains a permanent, searchable record of conversations. Sure you get the long-winded amateur novelists sending you page long emails, but for the most part I find it entirely manageable for the 40-100 emails per day I tend to get (which I acknowledge is not a lot, but my system held strong at 300-500 per day – which is definitely above average I’d bet).