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Good gaming rig?

Yes its good, on that budget Id personally get this:
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Xeon E3-1231 V3 3.4GHz Quad-Core Processor ($239.99 @ SuperBiiz)
Motherboard: ASRock H97M PRO4 Micro ATX LGA1150 Motherboard ($70.98 @ Newegg)
Memory: Corsair Vengeance 16GB (2 x 8GB) DDR3-1600 Memory ($107.99 @ Newegg)
Storage: Samsung 850 EVO-Series 250GB 2.5" Solid State Drive ($97.99 @ Amazon)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($52.49 @ OutletPC)
Video Card: Asus GeForce GTX 970 4GB STRIX Video Card ($332.49 @ B&H)
Case: Corsair 200R ATX Mid Tower Case ($56.98 @ Newegg)
Power Supply: XFX XTR 550W 80+ Gold Certified Fully-Modular ATX Power Supply ($61.98 @ Newegg)
Total: $1020.89
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-04-23 10:33 EDT-0400
 
Solution
Yes, this is nice.

Any suggestions to change it are just opinions really. There is nothing inherently wrong with it and all parts will work fine in that configuration.

You could consider the EXCELLENT Asrock mobos of recent. They are really packed with great features and are recommended far and wide, however that ASUS board is fine too.
 
Yeah its a great build, but I would much rather get the Xeon 1231, its pretty much a i7, without integrated graphics.

Overclocking is not going to get you as much potential performance. The Xeon is about same price, an d gets you the perfromance of locked i7.

unlocked i5 is great for gaming, but Xeon is still a stronger cpu and just as good for gaming.

If you do enjoy overclocking though, the i5 is great!
 
When I come across Xeon worshipping gamers I shudder and look to the left of my screen, where I can see inside my case, safe in the knowledge my unlocked i5 allowed me to OC to 4.6 stable and could probably even do more if pressed...

Stick to the i5 OP, the Xeon is a possibility, however not what I would recommend over the current all round favourite gaming cpu.
 
Yet many new AAA games out recommended requirments list an i7/or 8 thread amd cpu. That trend we will see more and more of.

i5 is a very capable gaming cpu, but you can still get better performance out of an Xeon or i7, over an unlocked i5, either way, for games right now you cant go wrong either way, even a g3258 oc to 4+ ghz get into same league as i3/i5/i7 in most any game out there. I just personally would choose the Xeon, its same price you get 8 threads, almost identical performance in ipc, and you dont have to worry about a coooler, temps, or life of the cpu, and most likley stand the test of time better than an unlocked i5, though its all in the lottery in the chip you get (note Xeon cpu are usually binned as server rigs and as such tend to be to last longer)