I don't have an agency suggestion, but I've worked with a number of CMS solutions.
We are on the Ingeniux CMS at the KU School of Medicine/KU Medical Center, but our internal web devs have done the work setting it up with assistance from the Ingeniux team. I use it daily to create and update sites. Their site is https://www.ingeniux.com/products/cms.
I've worked with WordPress, Squarespace, Joomla, and some others. They all have positives and negatives.
I see a lot of small hospitals on WordPress still, which can be secure with various add-ons and auto-updaters and such. But I do recommend having someone full-time (internal or external) that makes sure it's up to date and that updates aren't breaking functionality.
I use SquareSpace a lot when creating sites for teams of one, as it offers a lot for a flat price and it's nearly as easy to update as a word document. Drag and drop with easily customizable CSS. I can train it in a few hours. You can also hire developers to customize all aspects of it, so you don't necessarily have to be hamstrung by predefined options or plugins. Some of them offer ongoing support and they are all listed on Squarespace's site. https://www.squarespace.com/designer/home/