G4560 will want a lga1151 motherboard that will use DDR4 ram.
Some will use DDR3, but the DDR3 ram needs to be low voltage 1.35 ram, not the common 1.5v ddr3.
The apu is decent so long as you NEVER plan to upgrade it.
You buy a APU for the excellent integrated graphics.
But, there are no real good upgrades, particularly for a gamer.
If you install a superior discrete graphics card, you will have thrown away the big advantage of the APU.
Then, you are left with a relatively weak cpu. Most games depend on only a few fast cores.
Bottom line.....
What you get with a APU is what you will live with forever.
G4560 is an outstanding budget processor Perhaps $65.
A lga1151 motherboard can be about $50.
8gb of ddr4ram is about $60.
You can use passmark to roughly compare the performance of processors.
Your E6700 has a rating of 1703 when both threads are fully utilized, and 995 single threaded.
By comparison, a G4560 has a rating of 5095 and a single thread rating of 1992.