Name-recognition: I'm sure there are a bunch of quality web-hosts, but if I've never heard of you, or you're new, I'm not going to use you. Hosting companies, especially small ones, routinely go out of business.
For hosting reliability and availability are the main requirements. If you're a company I've heard of I'll have an idea of how good you are. Most of the time people focus on price, via sites like "low-end-box" and the companies listed there are often just circling the drain before they go out of business.
In short: be sustainable, and demonstrate availability & reliability.
After all your competitors are things like Amazon's S3 (cheap, reliable), GitHub pages (free), and similar.