As someone who has been on the other end of these conversations, knowing market rates is good but dont bank on those. Its easy for a company to say "we dont pay that here". Market averages are just that, averages. High mixed with low.

But understand what you can be making somewhere else and what value you bring to the table. Go high, but not insultingly high because they will probably go low. Understand what your true bottom line is and hold it. If they reject it, let them know you are dissapointed in their offer and quietly start looking for another job. They wont pay you what you want and your best bet it go somewhere else.