2GB or 4GB VRAM ?

Solution
If you can get 4GB without braking your budget, then defiantly go for it. While 2GB is fine, there are some small cases where the extra 4GB helps.
4 GB's might come in handy on certain situations, so keep that in mind. Here is your approximate build:PCPartPicker part list / Price breakdown by merchant

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($64.95 @ NCIX US)
Motherboard: Gigabyte GA-B85M-GAMING 3 Micro ATX LGA1150 Motherboard ($47.98 @ Newegg)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1600 Memory ($54.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($49.99 @ Amazon)
Video Card: EVGA GeForce GTX 960 4GB Superclocked Video Card ($209.99 @ Newegg)
Case: Corsair 100R ATX Mid Tower Case ($39.99 @ Newegg)
Power Supply: EVGA SuperNOVA NEX 750W 80+ Bronze Certified Semi-Modular ATX Power Supply ($49.99 @ Newegg)
Total: $517.88
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-06-12 19:27 EDT-0400

If your not sold on Nvidia GPU's, here is a better option, IMHO:

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($64.95 @ NCIX US)
Motherboard: Gigabyte GA-B85M-GAMING 3 Micro ATX LGA1150 Motherboard ($47.98 @ Newegg)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1600 Memory ($54.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($49.99 @ Amazon)
Video Card: MSI Radeon R9 290 4GB TWIN FROZR Video Card ($242.98 @ Newegg)
Case: Corsair 100R ATX Mid Tower Case ($39.99 @ Newegg)
Power Supply: EVGA SuperNOVA NEX 750W 80+ Bronze Certified Semi-Modular ATX Power Supply ($49.99 @ Newegg)
Total: $550.87
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-06-12 19:26 EDT-0400

Obviously the G3258 is going to limit your options, but initially it should do fine for most games. I know there are some games now requiring 4 cores (i.e. Far Cry 4), but there might be more in the future (who knows).

If you want to have a bit more flexibility, here is what I'd look at (I believe FC4 is more friendly to 2 core w/HT than just a 2 core CPU - G3258):
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i3-4160 3.6GHz Dual-Core Processor ($108.99 @ NCIX US)
Motherboard: Gigabyte GA-B85M-GAMING 3 Micro ATX LGA1150 Motherboard ($47.98 @ Newegg)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1600 Memory ($54.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($49.99 @ Amazon)
Video Card: EVGA GeForce GTX 960 4GB Superclocked Video Card ($209.99 @ Newegg)
Case: Corsair 100R ATX Mid Tower Case ($39.99 @ Newegg)
Power Supply: Corsair Builder 500W 80+ Bronze Certified ATX Power Supply ($29.99 @ NCIX US)
Total: $541.92
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-06-12 19:32 EDT-0400

 
the 4gb one is typically for 4k monitors. The higher the resolution, the more memory the video card will use.

NOTE: More memory does NOT make it go faster. And that video card wouldn't have the power for a 4k monitor in gaming. You might want to look at tom's charts and look at the benchmarks at different resolutions (according to what YOU are using).