If you need to look at the available options, then there is a superb resource here at
http://www.opensourcecms.com. You can even try them out, as a user or as an administrator. I have become attached to Postnuke, secure and stable under high 'loads' , and for the 'mission control' look and point and click updates. I have installed a number of there CMS packages, and if you are looking for a relatively low gradient in the learning curve, then Xoops, E-Xoops, or Phpwebsite are good options. Again, the bottom line if to decide exactly what you need the CMS for, and what modules/options are essential in the package.
The only packages I have seen which tend to get 'banned' are cgi/perl installations. I have yet to see posts anywhere on the internet, relating to Postnuke causing problems. That said, there is a limit to what a shared server can take! It is virtually impossible to get a straight answer from any website hosting company as to whether they will present a server/load issue. ... unless they are banned outright. There is no universal definition of a high load either, other than that which starts to have a detrimental effect on other hosted sites of other users ( quite a few normally) on the same server. There are too many variables involved, so the absence of a straight answer is not entirely unreasonable. I have, for example, recently discovered that Moodle ( a VLE php/MySQL package) has been causing some problems here, with its excessive demands on resources, even with a relatively low number of users.