So to put it in relation to what you know. Ubuntu is an OS (Operating System), just like OS X on Mac. You need an OS to do anything on a computer/server.
Apache (or Nginx or ISS or ...) is a web server, which is essentially a program that runs on the computer - but the main goal of that program is to deliver content to the outside world.
You don't need to install anything on your local computer to run a server here on DigitalOcean - but you need a client program, so you can manage the server, but that's already included on OS X and it's called Terminal, which includes SSH (on Windows you would download PuTTY).
But unless you want to spend time on administrating a server and learning about the "engine room" - which might be a little much, when you're also starting to learn about front end development - then I would probably recommend that you start with a regular webhost (like SiteGround etc).
Running your own server requires a bit of skill and time, and you're responsible for maintaining, updating and securing the server - so some of your time would be dedicated to that instead of the front end.
When you feel like you want to dig deeper or if you feel constrained by a regular webhost, then something like DigitalOcean will be a great tool.
You could use the One-Click Apps to get up and running in a jiffy, but you still need to maintain the server - and for what you're asking for (a static site) it seems like overkill.