Generally multirotor props work best in the 1:2 range for pitch-to-diameter ratios. Your 1247s should be fine for 2814s. I fly 1247s on my 2810s and it works well. As for 3S vs. 4S batteries, you don't give the Kv rating for the motors, or the AUW for the aircraft, so it's impossible to tell. If they're 750 or higher, should be OK with 3 cells and 1247s for a sub-5 pound machine. it they are lower than this, 4 cells would be a better choice. If we had curves for these motors we could look at the results and pick the optimum efficiency point, (in G/W) and know that props can be one inch up or down from this point for fine tuning.