I opted for the integrated sink and "coved" (seamless) backspash for my Corian (the REAL thing, not the knockoff brands) when I had my kitchen redone about 8 years ago and am totally satisfied. Keeping the countertops and sink clean are a cinch. I use Bon Ami cleanser in the sink and occasionally follow up with a weak bleach solution. I'm careful with my stuff so I can't imagine having a problem with chips. Even though I watched a demonstration showing that you can set hot pans on Corian, I never do -- I'm sure my Mom would come down from heaven amid bolts of lightning if I didn't use hotpads!
My sink is the one that is "regular" depth on one side and about 11 in. wide (still fine for most plates) and is very deep and wide on the other side. My dish drainer "lives" in the deep side most of the time but it is great to have for big soup pots and for wrestling with those monster turkeys and roasting pans at Thanksgiving (the roasting pan sits right down in that side for cleanup). It's something to consider as an alternative to a "regular" sink.