CMSes are notorious memory (CPU) hogs and don't belong on shared servers as they're throttled by hosts so all accounts don't suffer.
There is one solution, however, which I've found ideal for a client of mine: WebHostingBuzz (.com or .co.uk - pick the tld which is appropriate as they have servers in many different locations) offers Specialized Hosting for WP, Joomla, Drupal, etc. While on a shared server, they limit the number of accounts and ensure adequate access to the CPUs to keep traffic moving. My client used Joomla without any problem whatsoever (except the common requirement to keep it up to date to prevent "script kiddies" from hacking out of date code - or plugins).
If you're looking for a testimonial for WHB, too, be assured that I have three accounts with them (shared, specialized and dedi) and rave about their FAST response times to problem tickets (which are generally requests for help rather than problems). They claim to be priced a bit higher for their top-of-the-line equipment and service but I've not seen anyone cheaper so I consider them to offer TOP products and service at a very low price.