8 - 15 is a fair range (15 being high and nice clean / farang spec / AC etc) under 8 will probably be a little rough but depends if you have time to paint things up and or wish to buy furniture etc..
Kathu is a good compromise and there are some small houses dotted about (loch Palm / waterfall side especially).. The 'Dulwich' shortcut makes a neat way of getting out to the bypass road north and is a good area for being fairly central..
The rental market is not very well catered to in agents.. Only high priced farang operated things work via the web with one exception..
http://www.houseinphuket.com/ run by Kuhn Welta seems to be a good service.. I have heard nothing but good things about her and she has fair prices.
Most rental homes are found by hunting.. Sings hung in Thai have the best rates so a Thai speaker (reader) is really helpful..
Lots of stuff available in Patong due to being quiet..