You can get the automatic scooters very easily in Phuket, almost at each shop/beach or restaurants.
The rent may start around 250-350THB for the 150CC, whereas they may charge 350-500THB for 200CC. If you are willing to rent a manual motorbike, it may rent as much as 1500THB+ for 600 or 800CC. You may have to be little patience to do bargain, especially if you hire for a week or 3-4 days.
-As per Thai law, they expect IDP (International Driving Permit) for driving in the Thailand. I took chance on relying on my Indian license in case I get stopped. Try not to break any rule, follow the lane, don't park with places having red/white strips on the footpath, always wear helmets.
-Record the fuel level and request them to mention on the receipt. You may have to fuel up before returning the vehicle. In case the petrol level is slightly below the mark, they may accept it.
-Some vendors ask to deposit the original passport, which I would suggest to avoid. Even I end up giving original passport as he didn't agree, but luckily nothing happened when I returned the vehicle.
Try to request them to just take a photo instead of submitting original passport as I managed the other day.
-Few vendors don't have the full insurance, so in case of an unfortunate event, you may have to pay the full cost. I strongly suggest finding a vendor which include insurance too, even it may cost few bucks extra.
-Make sure you click photos of the vehicle while taking delivery so that vendor may not demand money for any existing damage or problem.
-Note down the vendor phone number and verify the return time/date availability.
I picked up 200CC automatic scooter which was good enough to climb up the hills with a pillion rider too. It cost me 350THB as I picked from the street near the Patong beach instead of renting from the vendors sitting on the beach :)