Pretty straightforward. I'm a designer looking to upgrade to a dedicated server hosting plan, but as the host does not manage the server themselves, I am wondering if I'll need outside help.

I can work my way around SSH and install apps and such, but don't know much about maintaining a server, if this is needed.

It depends what the web server does to the PC... if it's serving static pages and is set up then there is very little regular maintenance needed.

If the pages are dynamic and data is being delivered to the webserver (either from inside or from the internet) then you'll need to maintain it... check space usage, tidy up c**p, back it up, check for undesirable use etc etc.