GTX 1060 6GB is out of your range. If ok with 3GB you could go with the following build:Intel Pentium G4560 3.5Ghz 2-core/4-thread Processor 12,000.00 Gigabyte H110M-S2PH (DDR4) 10,500.00 Corsair Vengeance LPX 8GB DDR4 2666MHz stick 13,500.00 Palit Geforce GTX 1060 Dual 3GB GDDR5 39,500.00 Corsair Carbide-series SPEC 01 9,500.00 FSP Hexa+ 450 7,000.00 Seagate Desktop 1TB 7200RPM SATA 6Gbps 8,000.00 Samsung 850 Evo 120GB SATA 6Gbps Solid State Drive 11,500.00 However, you might have to flash BIOS for the 7th Gen processor to work. Get some professional help or go with 'Gigabyte B250M-D3H' mobo, which will add 4k to your bill.
I dont think we can max out GTA V on a 3GB card, but i think you can share some ram because no one needs 16GB and getting 16GB isnt hitting the price that hard
I dont think we can max out GTA V on a 3GB card
thus why everyone should avoid the 1060 cos its on par with 970 in most gaming scenarios. but much more pricier. the tomshardware GPU hierarchy chart clearly state this.http://www.tomshardware.com/reviews/gpu-hierarchy,4388.html