I am a computer science student with a project idea I am looking to build. How do I determine whether an app or a website is better to begin with?

I think you're asking whether you should go PC or mobile.

The answer depends on your interaction model. Think about a messaging app. The user will be interacting with it briefly but many times through the day. This is an ideal model for mobile. By comparison, an app that requires them to type extensive text or otherwise concentrate for some time, is better done as a "PC web" app.

Another consideration is focus. A todo list manager can be a very simple, focused app which is also ideal for mobile, as you need to be very parsimonious when you lay out your screens on mobile. Look at Clear, an ultra-minimalist todo app for iOS. If you compare that to a complex groupware app like Asana, you can see that the extensive feature set means that it works better on PC rather than mobile.

If you want to talk more, we can have a call.

I always recommend starting with a responsive HTML5 site to do your proof of concept. This can help you get some of the server based workflow out of the way. Assuming that the app is designed to run as a cloud based service, you are going to want to have browser access regardless of the platform you build for (iOS/Android/Windows)

The advantage of the app is that you can take advantage of pre-built SDK's from the OS which may expedite UX/UI implementation.