It looks like you might be able to install SUMA there, but depending on your experience level and exactly how this service works, there might be a few tricks involved or some obstacles.
As a hosting service it offers PHP, MySQL, and SSH access, which are key features you require. The primary obstacles are going to be what rights you have in the hosting environment and if all of the required software are installed at the required versions (the cURL, mbstring PDO and DOM modules for PHP, PHP at 7.1+, and the Zend Framework at 1.12.20). On a server you run yourself, or a virtual server that you can get from a service (like Linode or Digital Ocean) you would have root privileges allowing you to install arbitrary software. I don't know what the process for getting software that's not installed added or if the software you need is already there.
If it's already there, then you'd need to use the SSH access to get the SUMA files onto the server into the right place and set privileges on them appropriately. You can upload files to a server using SSH via a protocol called SCP and there's a free piece of software for Windows called WinSCP that makes that fairly easy. To do all of the command line stuff required you'd use a regular SSH client, like PuTTy.
You'd probably also need to use that to get the MySQL database setup properly, although that might be able to be handled via the console they offer there. Some of the instructions are likely to vary depending on the configuration of your environment on the server. The more you know about Linux, the easier it will be to figure out what you need to do to resolve those problems. However, it sounds like you probably have limited Linux experience, so that might be tricky.
Mark Swenson
IT Manager
Winnetka-Northfield Public Library District