Jump sizes of a compound Poisson process

Question

I have a Poisson process $(S_t)$ defined by $$S_t = \sum_{i=1}^{N_t} Z_i$$ where $Z_t$ are i.i.d. standard normals, and $N_t$ is a Poisson process. I have to determine

1. the set of all possible jump sizes
2. the distribution of the waiting time until the first jump $T_1 := \inf \{t>0 : S_t \neq 0 \}$
3. moment generating function of $S_t$

In the first problem I do not know how to define "all possible jump sizes".

The second problem I start with $$F_{T_1} (y) = P(T_1 \leq y) = P(\inf \{t>0 : S_t \neq 0 \}\leq y) $$ But then again, have no idea how to proceed.

Any help would be appreciated.