Is (high) pressure required to form (quartz) crystals? I've been reading a lot of sources about the hydrothermal synthesis of quartz using autoclaves. I want to try doing this myself, but before I can I need to know the minimum pressure required.

If you need a refresher, hydrothermal synthesis uses steam as a solvent, and creates a supersaturated solution that places the quartz molecules onto a seed to grow a pure crystal.

I've gotten many different numbers in terms of how much pressure [from the steam] is required for the process, ranging from 7500 psi to 30000 psi. I want to work with as low of a pressure as possible.

So then my question is: is high pressure necessary for quartz crystal formation? My understanding is that the pressure in the case of hydrothermal synthesis is created from having large amounts of steam in order for more material to be dissolved in said steam, so the crystal will form faster. So is this the case, in which having a lower pressure will work, or is pressure required for the crystal to form properly? As in, does the pressure actually affect the crystal structure in some significant way?
Pressure does not affect the crystal structure (unless it gets insanely great, so that stishovite formation kicks in; that's not going to happen in an autoclave, though). Pressure, however, does affect the temperature (indirectly), and hence solubility, and hence the rate of crystal formation. There is no lower threshold, that's why you keep getting wildly different estimates for the "required" pressure. It is just that the higher you get, the faster your crystals grow. They would grow at normal atmospheric pressure as well, just very slow (so that only your great-grandchildren may possibly be able to see them).

I suggest that you aim at something less extreme. Calcite, maybe?