I'm not certain about luggage storage. I would not worry about taking any sort of transportation into town. The walk is easy and enjoyable, slightly uphill.
I go in and out of the Arezzo train station frequently and I have never seen a luggage storage area. However, I am going again tomorrow and I will have a better look around.
As for getting to the city from the train station - really nothing could be easier. Have a ready through my article about a circular itinerary you can do starting at the station.
