All Outlook mails are inside a file with extension .pst. So all you have to do:
- Install the same version of MS Outlook (or a later one) on your new PC.
- Set it up like you did on the old PC
- Copy the .pst file from the old PC (or from your backup!) over the (empty) .pst file on the new PC.

Outlook has more than email. For example, it can have an address book and rules to move spam mails to the spam folder. Those are in other files.
https://support.office.com/en-us/article/find-and-transfer-outlook-data-files-from-one-computer-to-another-0996ece3-57c6-49bc-977b-0d1892e2aacc tells where to find the data to copy (assuming you have Outlook 2007 or later).