Do I have to use Google Tag Manager if I just want to implement some basic GA tracking?

Not required. You are free to implement Google Analytics the old way by adding code snippets directly to the website’s source code. However, It is a good idea to implement Tag Manager because it gives you the ability to add and update your tags for conversion tracking, site analytics, remarketing, etc. There are nearly endless ways to track activity across your sites and apps, and the intuitive design lets you change tags whenever you want.