Figuring out the BEST hsoting is always a bit of understanding your site and how it’s set up ??
So your size is because of the manage-wp folder, which is 2+ GIGS! It’s storing all your backups, so yeaaah that could be a problem. You should nuke that and turn off that backup tool if you want to use DreamObjects Backup.
Looking at your plugins, you’ve got some things that are going to make your site slower because they’re not the most optimal plugins
All of these can be replaced by Jetpack (which is actually faster):
subscribe-to-comments-reloaded 150422
subscribe-to-comments-reloaded-better-unsubscribe 0.9.6
wordpress-popular-posts 3.2.2
yet-another-related-posts-plugin 4.2.4
You also have both better WP security and WordFence installed. I personally would remove them both and make sure ‘Extra Web Security’ is on in your panel, which will do much the same think with far less overhead. Wordfence in particular has been techy with DreamPress since it puts down cookies to check users for being real humans, and cookies can break cache because if someone has a cookie, they’re special and don’t need caches.
You’ve also got some ‘tendrils’ of caching plugins left in your wp-content folder (a cache folder, for example, and the file advanced-cache.php), but I don’t see an active caching plugin, so you need to make sure you always clean all that up.
And … you should try WP Super Cache. It’s really good on shared hosting, and something I personally recommend.