You could base the report on the standard Activity report which can be found at Reports>All Reports>Activity Details.
If you are not too familiar with how reports and report templates work check this chapter of the User Guide: https://docs.civicrm.org/user/en/latest/reporting/what-is-civireport/
Over-riding core file would be last thing we should do unless there are no other option, since you need to port the file in each incremental upgrade.
Instead I would do one of the below
To add filtes, fields etc to report i would implement hook_civicrm_alterReportVar via extension or module or plugin
If the requirement is too complex than i would create ...
I am not sure if there are any extension that you do your job using reports but you certainly achieve this via other methods
If you are on Drupal than you can use views to create the list by sorting created date by descending order.
You can also use Data Processor extension to create dashlet or search report with your own columns and sort by created date ...