I don't know anything about quartz but I've got matt (matte? too early aarrgh) white Corian in my rented flat. It's smart and very modern but I don't love it, I have to say.
It was already in when I moved in but I believe it's quite flexible to fit, and can be moulded to fit any shape or layout. Some people have Corian sinks too, moulded in a single piece along with the worktop, although I would imagine keeping one of those clean could be tricky. Mine is stainless steel.
This might just be me, but because the Corian is a thinner piece - mine is about 1cm thick - it can make the worktop area look mis-weighted, if that makes sense. It looks too thin for the cupboards.
It will stain if you leave staining things (beetroot, tea, turmeric, tomato sauce, blueberries; the usual suspects) on it, but I have some Barkeeper's Friend spray for stains which gets pretty much everything off. I've managed to keep mine white, but it does take a 'little and often' approach to wiping. I use a Method all-purpose cleaner most of the time which seems to work well. When it's perfectly clean it still looks pretty pristine.
The book of words that came with it says it's heat-proof to an extent, but not to put hot pans or dishes on it. So I use trivets.
Also, the matte finish smooths off slightly over time. The Corian was new when I moved in about 18 months ago and now the well-used areas are starting to take a slight shine. Apparently you can have DuPont or whoever come in and re-finish it, but I think it's probably got a few years before that needs to happen, and we'll be moving out within the year.
I think if I were doing my own kitchen I'd consider it over laminate and certainly over wood, but perhaps not in white.
In an ideal world I'd have granite; I had it in the last place I lived and I found it to be more attractive and easier to care for.