We just replaced ours with a Blanco Silgranit II in white. So far I'm very happy with it. We knew we wanted granite composite and after researching everything, that was the best brand. I know a lot of people like stainless steel and it's a great material, but I HATE water spots and the filminess they get.
Ooh I was looking at the composite ones. We have formica countertops though so I'm not sure if undermount works?
They come in undermount and top mount configurations. Beware that some of the brands have had durability issues, so I would Google for reviews before buying. There's one that is corian instead of granite that seems to have a lot of problems with cracking under high heat.
We have Blanco Silgranit (Precis) sinks in the kitchen. So far, I like them better than SS.
ETA: Ooopps! I just realized it doesn't meet your budget. On the faucet, check out ebay. I've bought single hole pulldown kitchen faucets on ebay for less than $100 (regular 2-4x what I paid) and used them in our laundry rooms and garage. Very satisfied with them.