A huge issue with SEO is site speed. Everyone wants to have a FAST site. Well, lets just boil it down for you. You can not achieve a fast site without a fast host. Hosting is the most important factor in determining your page load speed.
I’m damn good at optimizing sites. I can get sites to load ridiculously fast and pass all those speed tests and get the scores that look pretty on the GT Metrix reports. I can’t do it without GREAT hosting though. It is literally the backbone of your website. It is it’s home. If you are serious about your business and serious about your website invest in great hosting.
You’ll want to look for server level caching. I also look for free CDN with your site and SSL to be included.
Shared hosting is generally a terrible option. Those companies try to fit thousands of sites on a server. (That’s how they can give you such a cheap price.)
I’m not going to recommend any particular host here. I do have my favorites, but I will say if you aren’t happy with your sites speed. Look first at your host.