Dynamic IP is not a problem! You do need a static domain name, but you can have dynamic IP address and use one of the many places who will keep track of your server as your IP address changes. There are lots of these. dyndns.com was an early one and now. is dyn.com and bought by oracle it seems but certainly still doing dynamic DNS as a service. There are many others, some free.
You can get a domain form the ones they offer there, and then set up your server or your router (best) to report back to them whenever your IP changes. Then you are up and running. You need to install the server, and get a certificate for TLS.
You can buy and rent your own domain from anywhere, and then get dyn.com to start provide dynamic DNS support for that too. Then you have your own domain, which you can hang on to however the people you depend on to run services change. That is a good idea.
Of course when you get an account on solid.community you do get a domain name in fact … but ties to that community. One of the things inrupt has been thinking of doing is allowing you get us to provide virtual host service so that as well as your data being in that subdomain like timbl.solid.community, we also serve the same data as your own private domain. So lots of ways to go. And you can change which you use.
Of course you can move between these things, as solid allows you to copy all your stuff, including all the access control information, from one server to another.