A classifier for handwritten digits in the MNIST dataset is generally considered the "Hello World" of neural networks. I went over it in a course, but there are countless tutorials to be found online, i.e. https://www.digitalocean.com/community/tutorials/introductio...
Once you begin to understand how to handle data and how to define layers, you can start playing around with whatever your heart desires. The rabbit hole is vast and endless :)