Given p and r: Pick your favorite group $G$ of order $r$. It has a faithful transitive action on a set of size $m$ for some $m$, so you can take the semidirect product $\mathbb{F}_p^m \rtimes G$.
Given p and m: The group $GL_m(\mathbb{F}_p)$ contains a (say, Sylow) subgroup $G$ of order relatively prime to $p$, so again you can take the semidirect product $\mathbb{F}_p^m \rtimes G$.