I have three SUPs, one a 10 foot surf sup (corban), a 10'11" PSH surf SUP (great board) and a 14" race/downwinder board.
All depends on what you want to do if its Surf any of the 9 foot plus Starboards widepoints will suit your size and weight. If its racing touring look for a 12'6" or 14" race or downwinder board's but remember that you still need it light enough to get it on/off roof, store at home, carry to waters edge. A race or touring/downwinder will be faster on flat water and better for long paddles
My wife is similar size and can paddle a 9' surf sup no problems in flat water. Suggest you demo a few from shop to get a feel for what will suit you. Its a great sport I luv paddling my 14 footer along the coast on flat no wind days, I can see all the reef and fish and living in west australia spot the great whites sharks before they get too close.... (tragically we had another attack last weekend just up the coast) :-(
"Times fun when you are having Flies" Kermit the frog