The magnetic structure and phase diagram of the layered ferromagnetic compound Fe$_3$GeTe$_2$ has been investigated by a combination of synthesis, x-ray and neutron diffraction, high resolution microscopy, and magnetization measurements. Single crystals were synthesized by self-flux reactions, and single crystal neutron diffraction finds ferromagnetic order with moments of 1.11(5)$mu_B$/Fe aligned along the $c$-axis at 4K. These flux-grown crystals have a lower Curie temperature $T_{textrm{c}}approx$150K compared to crystals previously grown by vapor transport ($T_{textrm{c}}$=220K). The difference is a reduced Fe content in the flux grown crystals, as illustrated by the behavior observed in a series of polycrystalline samples. As Fe-content decreases, so does the Curie temperature, magnetic anisotropy, and net magnetization. In addition, Hall effect and thermoelectric measurements on flux-grown crystals suggest multiple carrier types contribute to electrical transport in Fe$_{3-x}$GeTe$_2$ and structurally-similar Ni$_{3-x}$GeTe$_2$.
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