We've been hosting with HostMonster since 2008 and we've been very happy with their level of service and technical support during that time. Unlike many other shared hosting, HostMonster gives amazing control. For example, you not only can choose which version of PHP you want to run, but can have different directories running different versions and have control over your php.ini file to make changes are increase limites.
If that means nothing to you, then HostMonster is a reliable hosting. Very rarely have this site, or other we've hosted go down (one time it was due to a severe storm near their data center and even then it was brief). There server and support staff are located in the United States so the communication barrier shouldn't be a problem. Get 3 years of hosting for less than $200 and if you sign up using our referral link, we'll move your site for $29.99*.
*- Conditioned upon verification from HostMonster.