With e-mail, just set up your Mac, iPhone, and iPad to connect to the same e-mail accounts.
Add email accounts in Mail on Mac - Apple Support
Add an email account to your iPhone or iPad - Apple Support
You probably won't have to specify all of the details of the connection – like whether to use IMAP or POP3. If you are accessing email from multiple devices, you want IMAP. With IMAP, the master copies of your email live on the email provider's server – your Mac, iPhone, and iPad may store cached copes, but they won't fight each other, to see who can grab a particular email and delete it from the server before the others can see it.
You can set up an iCloud Mail account, but this is not a requirement.
Send and receive iCloud Mail on all your devices and keep Mail settings up to date - Apple Support
Set up iCloud Mail on all your devices - Apple Support
The key is just to connect all of your devices to your e-mail accounts, and let email synchronize through your email providers (e.g., Apple for iCloud Mail, Google for Gmail, etc.).