New Installatiuon, Old Content

Hi, earlier this week I had some problems with my hosting provider. I had to change my theme because for some unknown reason Cool Stuff keeps crashing my site. I want to make a “clean” installation of WordPress in order to hace a fresh start on the site’s theme.
In order to do this I plan on uninstalling WordPress via DirectAdmin and then installing it again, but I want to know how to restore users, old posts and images. What folders do I need to upload on my FTP server? Do I need to restore the old database or a new one would be just fine?
If I need to use the old database, is there a way to uninstall WordPress without deleting it? Because Installatron keeps deleting it everytime I try.