Ah someone beat me for becoming the first to advice i7, well i have a bit different approach.
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i7-7700 3.6GHz Quad-Core Processor ($309.33 @ OutletPC)
Motherboard: Gigabyte GA-B250M-DS3H Micro ATX LGA1151 Motherboard ($73.98 @ Newegg)
Memory: G.Skill Ripjaws V Series 16GB (2 x 8GB) DDR4-2666 Memory ($89.99 @ Newegg)
Storage: Samsung 850 EVO 250GB M.2-2280 Solid State Drive ($96.93 @ B&H)
Video Card: EVGA GeForce GTX 1070 8GB SC GAMING ACX 3.0 Black Edition Video Card ($379.99 @ Newegg)
Case: Fractal Design Core 1100 MicroATX Mini Tower Case ($29.99 @ SuperBiiz)
Power Supply: EVGA 600B 600W 80+ Bronze Certified ATX Power Supply ($49.49 @ SuperBiiz)
External Storage: Western Digital 1TB External Hard Drive ($54.99 @ Best Buy)
Total: $1084.69
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-02-07 20:42 EST-0500
My build is $35 more expensive than yours, but I still included external 1Tb hdd as you wanted. But again I would recommend against it, better off using internal HDD as your SSD won't fit much.
i7, GTX 1070, 16Gb ram, M.2 gen 3.0 supported motherboard, M.2 SSD samsung evo, 600W certified psu and usb 3.0 front panel casing, all with $35 more expensive. I think its really worth the $35 upgrade. Here is the reason:
i7 vs i5. Do you know i5 have started to meet their end against new AAA games such as Battlefield 1, farcry primal, Mafia 3 and watch dogs 2. Here is a youtube link that show how i5 actually bottleneck since gtx 970
https://www.youtube.com/watch?v=s42gvVS77dU&t
Some conservative said its the game maker fault, they just do not realize its time to move forward. 4 thread optimization has started since 2012 (Tomb Raider) and its a wonder they expect better game but with the same hardware. Its the era of 8 thread.
You have M.2 slot, why make use of it?. It will save more room in that tiny case for another drive.
GTX 1070 6Gb vs GTX 1060 3Gb. no need to say more, right?
Don't worry about 600W 80+ bronze, it will do its job well against this build, even have extra room for overclock and add more device later.
Good luck