What were you running your site on up to now? Was it custom-written PHP or another scripting language? If you're getting close to overloading your current hosting plan, I doubt that going to a CMS will improve the situation -- I would expect your CPU load to increase with a CMS.

Drupal and Joomla, along with Wordpress, seem to be the Big Three of CMSs. Drupal is widely considered the most capable, with the most free quality add-ons available, at the price of a very steep learning curve. Joomla is quite popular, and easier to learn, but I hear many complaints that to get beyond the basic add-ons you have to shell out serious money. Wordpress is very popular, even though it's fairly lightweight as a CMS. It might do for your site (at least, don't ignore it). I would look at the add-on libraries for all three and see if they have all the components you'll be looking for for your site. Ask around for experiences doing the sort of things you're looking to do.

I can't speak to the Softalicious installation of any of these. All can be installed manually, so don't think that you have to do a One-button install. All three are free, so you can do some experimenting without risking anything but some time.

OK, but make sure your users are reasonably computer-savvy. Updating pages, even with a CMS, is not the simplest thing. A CMS gives you lots of flexibility in what to do with a page, i.e., plenty of rope to hang yourself. Are these "users" the site administrator(s)? You will probably have to give out the master password to the site to anyone allowed to edit it, so you don't want to spread that too far.

A Wiki is designed from the ground up to be updated by many people (general public or password-controlled), but I'm not sure you will be able to do the specific layouts you want. Have you considered just what parts of the site need to be updated by your users? If it's all text, and relatively small segments, you might have a password-access form to update certain pieces of text, storing it in a database or even a flat file. That would be done in PHP, but would give users fewer opportunities to shoot themselves.

A CMS (or even a hand-coded PHP site) will definitely use more resources than a static HTML site. The only way you'll know for sure is to try it out. If LP suspends your account due to excessive resource usage (CPU load), you'll know you went too far* and you'll have to fall back to your old static site. That would be a shame to have put all that work into a CMS, only to be unable to use it without upgrading to a VPS or even dedicated server! At least, you'll have learned how to work with a CMS.

*I wish, I wish, I wish that LP would give its customers a way to monitor their resource usage, so they could take corrective action before being shut down.

Drupal is considered the Mercedes Benz of CMSs. They do require that you periodically upgrade the Drupal software as PHP and other components are upgraded. As almost everything is kept in the database, this is generally not too painful. I presume that Joomla and Wordpress behave in a similar way. Any major package like this will keep up with PHP and MySQL changes. Small, poorly supported software might not get upgraded very quickly, but I wouldn't worry about the major players.

By all means, make a test installation of Drupal or another CMS, and play with it. You may find it wasn't as much work as you feared to bring up your site using the CMS, or you may find it overwhelming (especially Drupal).