So Mail is exceedingly slow on my Mac. I want a client that is a bit lighter than Mail, and also actually notifies me of messages when the app is closed (if it's doable, I'm not a coding master).
Depending on how many messages you get each day, one option is to rely on your phone to alert you when you've got a new message. A quick glance would tell you whether it's worth firing up Mail to read a new message. I use that technique for an account where I get fewer than a dozen messages a day.
There are a couple of recent threads about the pros and cons of Outlook and Thunderbird. Thunderbird is free, so you're not out any money if you try it and don't like it. Outlook might be free if you have an email host that provides it as part of an IMAP or Exchange plan.