From the menagerie of neural networks architecture’s, why start with building an autoencoder? There are two good reasons.
Autoencoders illustrate the thing that makes neural networks special. They can combine inputs in unexpected ways to create useful features. Autoencoders use this capability to find simple representations of complex inputs. They identify a set of patterns that describe their input well.
The other reason is that autoencoders make it really easy to see when the neural network has found the right answer. And when the network is wrong, autoencoders clearly show just how far off it is. The output, when it’s behaving well, looks exactly like the input. And when it’s not behaving well, you can look at the output and see where it’s failing.