You can use ZeroTier if you need to traverse a NAT or don't have a static IP and you don't want to deal with DynDNS. That's what I do to access my work computer. It's free and works perfectly.
Yes, a lot. but I don't really have a permanent location to store the server unfortunately.
I'm not the person you posed the question to, but what's the secure, convenient way to do that? If I want to ssh into my desktop from within my house? If I want to ssh into it from elsewhere?
Am I missing the question? Maybe, maybe not. The simple answer is build your new "server" and install some version linux, like Ubuntu. Set up the accounts and make it so you can login using a private key. Turn off remote login with password so that you can only login with the private key. Install Fail2Ban to block automated hacking attempts---almost the second you expose your server to remote traffic you will start seeing attempts. Configure your internet router so that incoming port 22 traffic is routed to the server (or all ports if you don't care about security). Signup for a free dynamic DNS service for when your IP changes. Now you can login to your home server from anywhere using a your hostname which is tied to your home server external ip address. Its secure because there is no password to brute force and Fail2Ban is killing external attempts. You can secure it further using more research, but this is the basic answer.
Nope, you aren't missing the question. That's just a lot of stuff I didn't know to do (or how to do). Thanks!