The weather in September can be perfect. Nice day time temperates and comfortable night temperatures. There is always a good chance of some rain sometime during September as the temperature drops from the very high to the not so high, there is usually a big storm but this only lasts a day or so and then the sun comes back again. It will still be quite busy at that time of year and everything will be open.
I've been twice in October and it's still been shorts weather in the daytime and occasionally a light coat at night, I'd expect September to be warmer. Trips etc will depend on the ages of the people in your party, my advice is to try and get hold of leaflets from various trip organisers, decide what you want to do then go round and compare prices. Remember this is Turkey so prices aint fixed!