For more deserted beaches I would choose a location between Surin and the airport. Bang Tao beach (the "Laguna" area is very nice with good beaches) or Nai Thon beach (it may be spelled as "Naithon" too). There are several nice resort properties near/at these beaches, and maybe you are lucky to find low-season rate within your budget (a part from that your budget is more suitable for a mid-range Karon or Kamala/Surin hotel)

If you expect to have the beach to yourself I would not stay in Karon/Kata beach.