Which motor would work best as a generator?
What size do you consider "medium", in say kW or W? What style wind turbine is it- fast rotational or slow?

You could use an AC motor but you would likely need a gearbox to ramp up the rotational speed of the power transfer between the wind turbines main propellant shaft and the motor. 
AC motors are indeed cheaper (due to mass manufacturing and the common place nature) but have a higher operating speed. What type of AC motor are you looking at too? A synchronous machine or induction?

A DC motor is probably the best bet for your application because the world of motors can be quite complex. A controller will be needed to charge your batteries and to prevent over charging and excess power dumping. 

Also yes, a single phase ac motor with bridge rectifer would be able to do such but see above queries!