No to your A8-7600. It's ridiculously outdated despite its supposedly quad-cores-ness its performance is just several leagues below an Intel i5; and with AMD already released Ryzen on AM4 socket it's also at a dead end, and it only support DDR3 not DDR4. I don't know what hardware you already had and can be reuse in this build, so:
At up to 900 USD and to include most of everything you'll need to get the build going:
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i5-7500 3.4GHz Quad-Core Processor ($204.99 @ Newegg)
Motherboard: ASRock B250M-HDV Micro ATX LGA1151 Motherboard ($56.98 @ Newegg)
Memory: Team Vulcan 16GB (2 x 8GB) DDR4-2400 Memory ($94.99 @ Newegg)
Storage: SK hynix SL308 120GB 2.5" Solid State Drive ($49.49 @ SuperBiiz)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($54.99 @ Newegg)
Video Card: MSI Radeon RX 570 4GB ARMOR OC Video Card ($179.98 @ Newegg)
Case: DIYPC DIY-F2-W ATX Mini Tower Case ($35.99 @ Newegg)
Power Supply: Corsair CXM 550W 80+ Bronze Certified Semi-Modular ATX Power Supply ($39.99 @ Newegg)
Monitor: ViewSonic VX2457-MHD 23.6" 1920x1080 75Hz Monitor ($139.99 @ Newegg)
Keyboard: Logitech MK120 Wired Slim Keyboard w/Optical Mouse ($14.99 @ Newegg)
Base Total: $895.40
Promo Discounts: -$5.00
Mail-in Rebates: -$25.00
Shipping: $6.98
Total: $872.38
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-05-02 02:07 EDT-0400
Prices are sourced from Newegg, which I would assume to be your preferred retailer. Except for the SSD, since Newegg is out of stock on that model.
This does not include cost of a Windows 10 license, which you can just install and run un-activated for, I believe, 30-45 days before it'll start nagging/degrading the experience.
With this config, you'll get an i5, a solid foundation performance for either gaming/media usage.
16GB of DDR4, enough for at least 2-3 years to come (gaming load; for general office/web browsing load it will be enough for the foreseeable future).
An SSD for the OS, so that you'll get a system that will be quick to start up, and responsive web browsing.
An MSI RX570 Armor together with the Viewsonic VX2457 for FreeSync support for smoother gaming/media usage.
A simple but decently size mATX case, mATX motherboard and a semi-modular PSU to allow you to have an easier time doing the cable (doubly important in cheaper case).
And a simple KB/Mouse set.
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