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Outlook talks to a mailbox over IMAP for reading and SMTP for sending, and both are available on every tier. The setup is short, and the part that causes trouble is almost always the same thing. Outlook's automatic configuration finds nothing and you have to enter the settings by hand.
That is not a fault. Outlook guesses at server details from the domain name, and a mailbox on your own domain does not have a guessable answer. Choose manual setup when it offers the choice.
What Outlook needs
The incoming server is an IMAP server and the outgoing server is SMTP, and your full email address is the username for both. The password is the one for the mailbox, or an application password if you have turned those on.
Encryption matters on both halves. Use SSL/TLS on the incoming connection and STARTTLS on the outgoing one, and let Outlook choose the ports from those two settings rather than overriding them. An outgoing server that will not accept your password is usually a port set to 25 when the server expects the submission port.
An application password is the better choice
Many accounts now require a second factor to sign in, and a desktop client cannot answer a prompt for a code. An application password is a separate password for one device, generated from the mailbox settings. It works in Outlook without weakening the account, and you can revoke it on its own if a laptop is lost.
Turn one on before you set Outlook up if the account uses two-factor authentication. Setting it up first avoids an authentication failure that looks like a wrong password.
The order to do it in
Create the mailbox, confirm you can sign in to the webmail, and only then add it to Outlook. Doing it in that order proves the address and the password work before a desktop client adds its own layer of variables.
If the mailbox does not exist yet, creating your first mailbox is the step before this one.
Sending from your own domain
Once Outlook is connected you can send, but the mail has a second journey after it leaves you. The receiving server checks whether it is allowed to claim your domain. Three DNS records decide that, and adding SPF, DKIM and DMARC is the job that stops your mail landing in spam.
Set those up before you send anything that matters. A mailbox that works perfectly and a domain that has not been authorised to send from it look identical in Outlook and behave completely differently at the other end.