Can not offer specefic advice for the ashburton area, but the species you would expect to catch would be typical of east coast south Island. These include several species of shark and rays. The better eaten sharks being Rig (lemon shark) and Elephant fish. These are more common during the warmer months.
The most common fish caught would be Red Cod with the odd Kahawai caught during the summer. To keep things interesting other species would be caught from time to time.
You are to far south to catch Snapper and Kingish. It is not impossible but highly unlikely. I beleive if you search the fourms you would find a thread on fishing Dorie Beach.