Compound Poisson with Gaussian Jumps

Let $N\sim\mathrm{Poisson}(\lambda)$ and let $Y_1,Y_2,\dots$ be i.i.d. $N(\mu,\sigma^2)$, independent of $N$. For \[ S=\sum_{k=1}^N Y_k, \] derive the MGF of $S$, and compute $E[S]$ and $\mathrm{Var}(S)$.