If the maximum is 9700 lbs. that is not the amount I would expect the truck to tow on a regular basis up mountain grades and in the deserts and at high elevations. You may be able lift and carry a 100 lb. backpack but you do not want to carry that amount of weight all over the sierras.
I would also allow for passenger weight in the cab and water, etc. in the holding tanks, extra batteries, and other items that are not included in the trailer manufacturer's published weight figures.
I would also take into consideration the high 3.55 gears of your truck which help Ford to get a better EPA highway mileage number but hurt the truck's towing ability. Acceleration getting into traffic on a freeway or passing a tractor trailer rig going 20 MPH up a steep grade or even grade control with engine braking is going to be compromised with the 3.55 gears.
Your truck is at the bottom end of the tow vehicle spectrum and the trailer choice should be matched as you are attempting to do. Personally I would keep the dry trailer weight under 5,000 lbs. and expect that when fully loaded for a trip it will weigh about 6,000 lbs. which is a comfortable weight to be towing with your truck.
With a trailer my primary concern would be that there was adequate space for everyone to comfortably sleep you and your fellow travelers. The "sleeps 4" often means two adults and 2 small children and not 4 full size people. I would also check out the holding tanks' capacities as this can affect how long you can camp at spots where there are not full hookups.