Aero fully supports HTTP/2 but doesn't have automatically generated response.push calls yet. In the future styles and scripts will automatically be served via the push mechanism if the performance proves to be faster than inlining (a recent test has shown that this is not the case yet).
Aero will automatically start in HTTP/2 mode if it finds a certificate in your security directory.
I recommend Let's Encrypt, it's a fantastic service.
Simply drop the key and the certificate into your security directory.