I think you should be able to do it in one go, but you should definitely clone the server and do a test upgrade first particularly with that many versions (and of course back everything up first before doing the upgrade of the live site). I don't think you need to upgrade WordPress, but personally I would do this to the latest version immediately before or after.
Something I would check is the version of MySQL as I got caught out by that and version 5.7.5 is recommended. Version 5.6 needed setting changes that I couldn't make on my shareed hosting service, but 5.7 had the necessary settings by default.
Worth a look at the installation requirements at https://docs.civicrm.org/installation/en/latest/general/requirements/