How to optimize for a niche directory?

Howdy, My idea is probably common and I'm sure there are many naysayers ready to disregard my domain idea. I'm not asking for an opinion, this is a technical question.

I'm interested in how to best optimize my site speed and response so that I can have quick load on pages. I don't have fancy technology, I'm using wordpress, this is a page description directory. I'm on shared hosting. I don't understand the technical hard coded SEO. I'm creating pages as profiles. Blogs/articles are separate workflow, ofcourse. This is basic wordpress and I want my website to load fast, on a smartphone, with 3 bars of data. How can I best get this done?

Thanks