My website speed is very slow as well as my wordpress admin. Until now I've used a shared host solution at ovh.fr (For around $40 / per year).
I'm not sure if I should try to find another shared hosting in another provider (for a maybe better performance) or going to more expansive solution like wpengine.com
My website is a simple agency website with ~20 articles & pages. My wordpress theme is a premium one from theme forest (I'm targetting only the french market). Also, I installed W3C and other apps to increase speeds without having good results.