I think that shared hosting is fine, and no, I don't believe that you have to have dedicated IP addresses or unique Class C ip addresses, unless you are trying to hide something.
To this day, pdxtc.com remains on shared hosting with a shared IP address with dozens of sites, and seems to rank just fine, on page 1 for "search engine expert" and "internet consultant" etc. Matt says they no longer penalize IP blocks when one site is a spammer, so I think the only danger with shared hosting would be the shared mail server getting blacklisted due to the nefarious activity of another hosting client.
As far as different class C's go, do you have an interlinked network of websites, feeding your own backlink profile? If so, then yes, you would want to reduce that visibility by spreading out C classes to hide that network. It's not natural to have all your links come from one host.