Cover up mistakes upgrading hosting (thinking things magically will be ok) it's not always a good move and not (for sure) a good point to start. You can have any hosting you want, but if you don't know how to use it (and how to use and optimize your PS) your website will always be disappointing. Not maybe for you, but for your users for sure. Fill your PS with junk everywhere and no hosting will saves you from a bad site. Meanwhile, a good optimization (and a good use of what you got and how use it) we'll always save your site, also on a cheap/shared hosting.
Danny