"Will a Sata III SSD work in this laptop? If so, which models work best with this Apple hardware?"
Yes. I don't know.
"If I go with a non-SSD solution, any recommendations on which 1TB drive to use?"
I personally would opt for the Samsung or HGST.
Look at the following page from the OWC website. Any of the SATA HDDs and SSDs will work with you MBP. I would call the OWC technical staff and get their thoughts on the SSDs. (SSDs currently are too expensive for my needs) I recommend them as a place to purchase mac compatible equipment. They may not have the rock bottom prices but they stand behind their wares and are most helpful when it counts.
SSD Will work great with you MB and you'll notice some speed if you're planning on making it your main drive.
Although I am partial to OCZ, some models have issues with MB's. I had problems with the OCZ Vertex and OCZ blames my MB and not their drive. Installed another brand and it works great.
Sandisk, Crucial, Corsair and Kingston are some SSD's that works great with MB.