There are thousands of third-party email solutions on the App Store.
I leverage the built-in app to fit my needs:
1. Set up accounts as normal
2. In notifications turn ON banners, show in Notification Center, and show on lock screen.
2a. Notification settings mirrored on watch.
3. Set fetch to 15 minutes if IMAP gmail account, for example.
When a new mail comes, I can swipe down for a preview or see it on my watch and flag or archive it right away. No third-party app needed.