If you can work from the command line (and assuming you have a linux server) then SSH is simple – really all it does is give you a secure connection to the command line. You should get familiar with it because if something goes wrong with your server that may be the only way you can connect to it.
Next you need tools to transfer files to the server. While wget is useful for grabbing stuff from other web servers, while something like scp can get you to any host that also accepts ssh. I use this all the time to transfer files between home and work. Or you might set up an sFTP service to accept a GUI connection from a client like FileZilla.
As for what you can put on your web server… Well if you install php then you can run any php code. If you write javascript code then the web browser interprets that, so nothing to add to your server, but NodeJS code would require some installation. You also want to take some time to learn about security practices. For example if you have pages that use a database, an attacker can write a URL to gain access to your server if the code simply accepts any random input. There’s not really any limit to what can be run, but some things (like the php example) require you to install more components on your server.
Alternatively, there are also functional services you can run that have nothing to do with web pages. For example, a caldav service would allow you to host your own calendar that can be shared between multiple people or locations. Or maybe you want to start up a chat server like IRC or Matrix? Maybe you want to start a Mosquitto server for your personal IoT content? Think of it this way – literally anything and everything that makes the internet run is something you can host yourself.