How to build a secure AE scheme with generic composition?
You might look at EAX mode, which combines a block cipher in CTR mode with a CMAC.  However, EAX does differ from generic Encrypt-than-MAC in that EAX uses a single master key, which would be an absolute no-no for Encrypt-then-MAC.  Normally using the same key for both purposes is quite dangerous, but EAX is explicit about the use of the master key for the cipher and MAC, and EAX comes with a formal proof of security for that usage (and the entire mode).

Given that EAX (and CCM to a less flexible degree) provide a proven method for encrypting and authenticating data, for practical purposes my advice would be to just use one of the well known and trusted AEAD modes.

For theoretical purposes, the answers to Why choose an authenticated encryption mode instead of a separate MAC? and Should we MAC-then-encrypt or encrypt-then-MAC? should give you a good idea of the steps required to define a your own general composition, and how tricky it is to get all of those right.

The EAX paper also describes and proves the security of an EAX2 mode, which is a generic composition approach to create a two key AEAD mode based on a cipher and a MAC.