I guess you want your PC to play. Otherwise, the GTX 1060 3G would be excessive. I also assume that your monitor is FHD.
The G4560 is a bit weak for a GTX 1060 3G. In many cases you will find a bottleneck. I would not recommend a Pentium 2c 4h for a GPU better than GTX 1050 TI.
Note that the H110 mobs, in general, do not natively support the G4560 and require a BIOS update. If you do not have a 6th gen CPU, you must request that the BIOS be updated. This service some providers do for free but others charge 20 $ -30 $.
If you want to stay is Pentium, I would recommend a pentium of the 8th gen. like the G5400 and an H310.
The I3-8100 is a much better CPU to play with a GTX 1060 3G or 6G. It has 4c and also the AVX2 instructions that the pentium lacks.
It is difficult to predict the future, perhaps in a couple of months GPUs will be more affordable. In fact since April they follow a downward trend. If in this period the new generation of nvidia is confirmed, perhaps it could be obtained at a better price.