The number 1 thing I'd do is find customer reviews of the host.

I used to work for a company that required very high reliability, so I would always call and talk to someone. I would have them transfer me to a tech and ask him about their systems; backup power/generators, internet connections, redundancy, fire suppression, how many 9s, etc.. this was mostly to get a feel of how well-established and professional the facility was, and to try and guage the level of knowledge and experience of the random tech I talked to. Most of these hosts were international, which adds a certain element of uncertainty, as well.

However, customer reviews are probably the best test of overall quality, especially of their customer service.