Will a weak motheboard bottleneck a gud cpu and gpu? If theres such a thing.
I plan to get an i53350p or a 3470 paired with a gtx 760 or HD7870 gpu, but dont want to spend too much on expensive high end boards since the cpu and gpu is already above my budget. So will a entry level H77 or Z77 board suffice?
Since you are not going to overclock, an entry level board should be fine. Where you run into trouble with m/bs is when you overclock and the vrms cannot take the load. That said, most entry level boards are also a little weak in the power supply for the gpu pcie lane. The cards you note are both aux power users so I think you will be ok.
If it were me, I would go just above entry level to an ASRock Extreme3 or ASUS LK type.