If you have the original files and original database, that is the best approach to get it up and running. If you want to upgrade WordPress, first get it working with the old version, then do in-place upgrades (after backing up, of course). Some of the original plugins may not be compatible, though, so be mindful of that.
If you're using a different domain name (e.g.,
localhost instead of
old.domain.com) then consider the steps given in Wordpress's guide to Changing the site URL. It would also be worth perusing Moving Wordpress.