I am visiting Turku in Sept and wondered where are the best bars and what I should expect to pay for a beer?

If you go to Turku and like rock you should absolutely not miss Rokkibari!
It would be a crime.

A pint of beer (0,33 l) in Turku costs from 2 euros up to 4 euros or so. big one (0,5 l) from 2,5 euros up to about 5 or 6 euros. Then there is the "Eurosize" 0,4 l which costs something in between. You could try the Finnish style "pussikalja"; buy a plastic bag (=pussi) of beer (=kalja) from a supermarket and go somewhere outside to drink and get drunk. If the police doesn't see you and take your beers, you will be "ready" to go to any bar downtown. You will save money and be like the others.. drunk.

To answer your question about which bars to go to.. hard to say. There are over 200 bars and restaurants in Turku.. it depends what you are looking for. You can once again try the Finnish style and go to as many as you can before you are too drunk to get in. Then go to a hamburger bar or kiosk and fight with the locals while cueing.