I assume quartz is formed under great pressure and at high temps. In short, what class of rock does this fall into (sedimentary, etc.)? Or, are such stones (including various semi-precious stones which are a variant of white quartz) in a class by themselves?
Quartz is a mineral, not a rock.
Quartz is a mineral not a rock so as far as I understand it is neither igneous, metamorphic or sedimentary.
Yeah, as others said it’s a mineral. It’s also a component of many types of rock.
Like the others said, it’s a mineral, and can be found in all three types: sedimentary (e.g. sandstone), igneous (e.g. granite), and metamorphic (e.g. metamorphosized granite such as some gneisses) rock.
Assuming we’re now clear on rock vs. mineral, quartz is formed originally in igneous or hydrothermal environments (hydrothermal rocks don’t really fit into the igneous, sedimentary, metamorphic categories-- they’re rocks that precipitate out of water that is derived from and/or altered by magma bodies). Quartz is a very hardy mineral, and so it is also very commonly found in metamorphic and sedimentary rocks (most of the world’s sand is quartz), but this isn’t where it crystallized originally. Generally the big crystals you might find lying around are going to be from magma bodies which cooled very slowly (pegmatites) or are hydrothermal.
I’m not. Okay, so quartz isn’t a rock because it’s a crystal. So what’s the difference between a rock and a mineral?
Rocks are made up of minerals and mineraloids.
Actually, I prefer orchestral music. 
Just make sure no one in this thread gets upset. We don’t want anyone caught between a rock and a hard place. 
Quartz is SiO2 (Silicon Dioxide) and is one of the most common minerals on Earth. It is impervious to all acids except sulfuric, IIRC, and is found in both right and left handed formation. It exists in two forms, alpha and beta quartz; alpha quartz is piezoelectric while beta quartz is not. If alpha quartz is heated to 573 degrees C, it transforms into beta quartz. It melts at ~ 1700 degrees C.
I prefer to buy my milk in quartz bottles.
If everyone is gneiss, that won’t happen.
Geologists give me the schist.
These jokes are very shale-low!
I suppose I should add at this point that sometimes quartz thinks so much of itself that it acts like it’s a rock. When this happens, it’s called vain quartz.
Quartz can be embarrassed quite easily. When it does, this is known as rose quartz!
Comedy gold!
I should add I thought minerals of being things more like ores. So, what are ores classified as?
From Wikipedia: