If you just want to add logging to existing operations, reinterpret them at the call site. Something like this

    newtype LoggedStateT s m a = LoggedStateT (WriterT s (StateT s m) a) 

    instance (Monoid s, Monad m) => MonadState s (LoggedStateT s m) where
        get = LoggedStateT $ do
            val <- lift get
            tell val
            return val
        put s = LoggedStateT $ tell s >> lift (put s)

(which is basically an ad hoc effect system)

If on the other hand you want to reproduce the behavior of other languages, throw everything in `MyAppMonad` give it whatever capabilities you need.