I have quartz (Zodiaq) in the kitchen and love it for its low maintenance.
My friend's Corian got ruined when her MIL (who has granite counters) put a hot casserole dish directly on it. The damage was too much to just be sanded out. Boy was she mad, because they had just remodeled that kitchen.
One thing about quartz is that despite its speckled appearance, it really looks "frozen" compared to granite which often has direction or movement in it, so that is entirely a personal aesthetic decision.
There's a huge range in price for granite, there's colors considered lower grade (and even that varies depending on who you buy the granite from) to more pricey and exotic granites. If you go the granite route, I'd for sure go personally to pick out your slab. Other people's version of "oh, that little blemish is no big deal, it's fine" may not be the same as yours.
Through big box stores or well-known countertop businesses around here I'd see prices on the order of $60/sf installed for quartz and granite and it goes up (~$120/sf depending on the grade) from there. You get dinged for sink cut-outs (often $100-$200), sometimes faucet cut-outs, and your edge treatment (usually there are 1-3 edge treatments included with the basic cost) so be sure to ask the cost of those because it adds up. One thing to realize is that the actual cutting and polishing is done by a fabricator and it's they who tell the retailers what they charge for these "extras."
Now, sinks -- you should buy your own rather than go with whatever the countertop people say they have because almost inevitably you can get the same thing on eBay or
Amazon for a LOT less, almost 50% less (and you will faint when you see the cost of some of these sinks and the faucets). But get the brand and model# they are offering so you can do an apples to apples comparison (just say you want to look it up to see what it looks like).
A kitchen remodel will take up more of your mental energy and time than you would ever think. I spent
hours on the kitchen forum at gardenweb, trying to make sure I thought of everything...and there are still some things I didn't think of and realized after my kitchen was done. The #1 mess-up is that the underside of my countertop that sits on a raised bar didn't get polished, so every time I sit in my family room and look toward the kitchen I can see the rough ugly surface. I just never even thought that that was something I had to ask for! Grr.
That said, have fun with your kitchen remodel! It will be a worthwhile project.
Thought about Corian but my MIL got Corian counter tops a few years back and HATES them. She thinks they scratch too easily. 
