Good, experienced, real-world info from BPF on the use of flaps not outlined in the POH.
For the OP, I always use F10 for takeoff when flying the 172 with old 145 horse or newer 150 HP engine. Generally speaking, max lift/min drag combo with flaps occurs when flaps are set to the same angle as an aileron in max down deflection, which is pretty close to F10. This results in less runway used and prolongs tire life to a degree (and is much more comfortable with a rental aircraft that has an out of balance tire(s) with the attendant vibration after liftoff). Raise the nose a bit at the recommended speed and let it fly off when its ready. You can then milk the flaps up slowly after liftoff to improve climb performance when you have good speed. If heavy and with a turn required right after takeoff, F10 will also provide a bit more stall margin while in a bank. It will also feel better if the CG is close to the aft portion of the envelope when you have make that slow turn.
Wish my son's 170B with O-300 had a F10 position. We use the F20 notch at sea level and milk them up after liftoff. At higher DA's on a hot day, that (F20 initially) doesn't necessarily work. One has to adapt...but then, that's flying.
The 185 specifies Flaps 0-20 for takeoff. I use F20 and raise them to F10 right after liftoff for an increased climb rate, then up when clear of any obstacles. The 300 HP allows the drag of more flaps and the tail comes up a bit quicker (by itself), which reduces drag and takeoff distance. A buddy uses F10 on his 185, but I think his wing washout is set differently than mine...but that's another topic. He also doesn't have WingX STOL, which might be part of the reason, although I used F20 before installing the kit.
Hope this background info helps with your decision.