Hi,
I am assuming you're in the US for this build.
If you can spend US$800 on a build, this is what I would suggest (it will be able to do 1080p @ 60fps Ultra on most games)
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD - Ryzen 5 1600 3.2GHz 6-Core Processor ($199.99 @ SuperBiiz)
Motherboard: MSI - B350M PRO-VDH Micro ATX AM4 Motherboard ($74.49 @ SuperBiiz)
Memory: ADATA - 8GB (2 x 4GB) DDR4-3000 Memory ($68.98 @ Newegg)
Storage: Western Digital - Blue 250GB 2.5" Solid State Drive ($89.89 @ OutletPC)
Video Card: PNY - GeForce GTX 1060 6GB 6GB Video Card ($279.99 @ Dell Small Business)
Case: Corsair - 100R ATX Mid Tower Case ($39.99 @ Newegg)
Power Supply: SeaSonic - S12II 620W 80+ Bronze Certified ATX Power Supply ($41.89 @ Newegg)
Case Fan: Corsair - SP120 57.2 CFM 120mm Fan ($13.99 @ Amazon)
Total: $809.21
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-06-25 04:28 EDT-0400
Rationale:
CPU: the R5 1600 is good for more than gaming, but still perfectly good at it!
MOBO: Cheap and overclockable (which you can do to a decent extent with the stock cooler)
RAM: Fast ram is Crucial (pun not intended) for Ryzen, and 3000Mhz is a good mix of speed and price.
Storage:
SSD: 250gb is my personal favorite size for an ssd, as it can fit your OS and a sizable number of other applications and games.
HDD: your old Hard drive should be able to act as bulk storage
GPU: Honestly, don't buy the 970. It is no more powerful than a 1060 3gb and almost exactly the same price. The 1060 6gb is, in fact, slightly
more powerful than the 970. It is good for high-ultra settings @1080p.
Case: the 100R is a good case with only one major failing - it only comes with one fan.
Power Supply: a $15 rebate on newegg right now makes this a fantastic deal! It is reliable, and has a far higher wattage than you need.
Fan: the SP120 series are quiet and better than the AF series in most scenarios (https://youtu.be/LPFi5YEeqao?t=405)
If you want something that can do medium, then you can save a bit:
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel - Pentium G4560 3.5GHz Dual-Core Processor ($69.89 @ B&H)
Motherboard: Asus - PRIME B250M-A Micro ATX LGA1151 Motherboard ($67.98 @ Newegg)
Memory: G.Skill - Ripjaws 4 series 8GB (2 x 4GB) DDR4-2400 Memory ($59.92 @ Amazon)
Storage: SanDisk - SSD PLUS 240GB 2.5" Solid State Drive ($81.99 @ Best Buy)
Video Card: EVGA - GeForce GTX 1050 Ti 4GB ACX 2.0 Video Card ($134.89 @ OutletPC)
Case: Corsair - 100R ATX Mid Tower Case ($39.99 @ Newegg)
Power Supply: EVGA - 500W 80+ Bronze Certified ATX Power Supply ($36.88 @ OutletPC)
Total: $491.54
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-06-25 04:54 EDT-0400
Rationale:
CPU: good for a budget build, a nicely clocked dual core with hyperthreading
MOBO: Cheap and with 4 DIMM slots.
RAM: Speed doesn't matter here nearly as much as it does on Ryzen, so this is a nice cheap 8gb kit.
Storage:
SSD: nice and cheap, with a good amount of storage and decent speeds
HDD: same as above build
GPU: good for medium-high @ 1080p @60fps, the 1050 ti is a good value card
Case: ^^^^^
Power Supple: good enough for your needs, with good efficiency and reliability
Notes:
The 970 isn't a very good deal, probably best not to get it
The old case is probably best not used, as it will likely have sub-par airflow and compatibility
Any questions feel free to ask