What should I learn to make a note taking app?

It needs server side scripting to get notes from the database at a later point, so yes you'll need some type of RESTful app.

I would recommend using WordPress. It will provide the backend to save the information, and also allow each user to log in. Specifically, I would recommend the WordPress track, if you aren't familiar with it, to get up and running. If you are looking to build your own solution, then follow that up with the WordPress Plugin Project here: http://teamtreehouse.com/library/how-to-build-a-wordpress-plugin From there you can then build your custom plugin. This won't cover all aspects, like custom post types, but it will get you 75% there. And getting the other 25% from other online tutorials and the WordPress Codex should be easy enough. :)

I imagine that the main goal is to get experience for you. If you aren't a web developer, and don't want to be one, then you could look at making iOS or Android apps to do the job. However, know that you will always have to create some form of API that goes over the web, so you will always have to deal with that aspect.

If the educational aspect is secondary, you could always see if someone else has made a plugin for WordPress that fits your bill. But this sounds like a great little starter-project that has growth potential that will further your knowledge immensely.

Best of luck! ~Mike