How to design a non inverting op amp adder for my circuit?
Note that just two resistors actually gets you a good way to your goal:



When R1 = R2, OUT will be the average of V1 and V2, which is just your desired V1+V2 / 2.  Therefore, all we have to do is amplify by 2:



The gain from pin 3 to OUT is 2 when R3 = R4.

There are still some tradeoffs to make and issues to be aware of, however.  We know that R1 should be the same as R2, but what absolute value should those be?  This depends in part on what V1 and V2 can drive.  To minimize load on V1 and V2 you want to make R1 and R2 as high as possible, but if you make them too high the node on pin 3 will too easily pick up stray noise, the leakage current of the opamp will create a relevant offset voltage, and the inevitable stray capacitance on that node will form a low pass filter.  Unless you need very high bandwidth, 10-100 k&Omega; will be good value for most cases.

Note also that this circuit does not isolate V1 and V2 from each other as a summing inverting amplifier would.  Each sees the other with a impedance of R1+R2.  Maybe that doesn't matter, but you need to at least think about it.

As for R3 and R4, you make them lower to support higher frequency, but not so low as to overload the output of the opamp or drain too much current.  For example, if R3 and R4 are 1 k&Omega; each and the output often sits at 4 V, then this will eat up 2 mA of supply current.  That is probably irrelevant if this is part of something like a TV, for example, that is plugged into wall power.  However, 2 mA can make a significant difference in a battery operated device.  I'd probably again use 10-100 k&Omega; for each of R3 and R4 unless there is a good reason not to.