Okay, first be advised that you have an FM2/FM2+ mobo/CPU, not an AM2. The two are separate and not compatible.
Using some guess work on models I put your current system into PCPartPicker to see general power draw. The one major item that you didn't provide is the case make/model, with a mini-ITX build space compatibility is going to be a big concern.
PCPartPicker part list:
https://uk.pcpartpicker.com/list/KBNVHN
Price breakdown by merchant: https://uk.pcpartpicker.com/list/KBNVHN/by_merchant/
CPU: AMD A8-6600K 3.9GHz Quad-Core Processor (£89.04 @ Amazon UK)
Motherboard: MSI A88XI AC V2 Mini ITX FM2+ Motherboard (£82.97 @ Ebuyer)
Memory: Patriot Viper 3 8GB (2 x 4GB) DDR3-2133 Memory (£54.99 @ Amazon UK)
Storage: Samsung 850 EVO-Series 250GB 2.5" Solid State Drive (£89.00 @ Amazon UK)
Video Card: MSI Radeon R7 260X 2GB Video Card
Power Supply: FSP Group Berzerker 500W 80+ Bronze Certified ATX Power Supply
Total: £316.00
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-03-07 12:45 GMT+0000
Okay, building on what mitch074 suggested, I see two paths too
1) GPU only upgrade with overclock of your APU. Now you have a pretty decent 120mm AIO liquid cooler so no need to upgrade. In fact, with a mini-ITX build this is about as good as it gets. Watch your temps in this mini-ITX build.
But I pick a different path for graphics. The RX 460 is only two tiers above the 260X and you might not see a big difference in performance. As well, if you try to crossfire the APU then you have to match the discrete card performance to the iGPU on the APU
http://www.tomshardware.com/answers/id-2126330/apu-gpu-crossfire-compatibility.html
http://www.cpu-world.com/info/AMD/Recommended_graphics_cards_for_AMD_dual-graphics.html
Better to get a GTX 1050 Ti which will pair well with the A8-6600K.
https://uk.pcpartpicker.com/products/video-card/#c=380,377&sort=a8&page=1
http://www.videocardbenchmark.net/compare.php?cmp%5B%5D=3595&cmp%5B%5D=3557&cmp%5B%5D=2701
http://www.tomshardware.com/reviews/gpu-hierarchy,4388.html
I would go with this one
https://uk.pcpartpicker.com/product/NndFf7/zotac-geforce-gtx-1050-ti-4gb-mini-video-card-zt-p10510a-10l
And if you are not relying on the iGPU then you can reduce the load on your RAM so you could skip the additional RAM if really needed to. 8GB is today considered a minimum but still playable. You have two slots, I assume they are filled.
2) Upgrade the CPU/mobo/RAM/GPU. This path while more expensive will produce a much faster machine. I think the best path right now for budget builds is with Intel Kaby Lake Pentium processors and not Ryzen. The reason is that Intel has enabled Hyperthreading and now they sport 4 threads but a very low price. The G4560 is that much faster than your A8-6600K.
http://cpu.userbenchmark.com/Compare/AMD-A8-6600K-APU-vs-Intel-Pentium-G4560/m3344vs3892
And we don't know when AMD will be releasing the lower end Ryzen CPU's. Here is my suggestion.
PCPartPicker part list:
https://uk.pcpartpicker.com/list/QRG4jc
Price breakdown by merchant: https://uk.pcpartpicker.com/list/QRG4jc/by_merchant/
CPU: Intel Pentium G4560 3.5GHz Dual-Core Processor (£52.34 @ BT Shop)
CPU Cooler: Cooler Master Seidon 120V 86.2 CFM Liquid CPU Cooler (£0.00)
Motherboard: MSI B250I GAMING PRO AC Mini ITX LGA1151 Motherboard (£99.80 @ Alza)
Memory: G.Skill Ripjaws 4 Series 16GB (2 x 8GB) DDR4-3000 Memory (£103.62 @ More Computers)
Storage: Samsung 850 EVO-Series 250GB 2.5" Solid State Drive (£0.00)
Video Card: Zotac GeForce GTX 1050 Ti 4GB Mini Video Card (£136.98 @ Amazon UK)
Power Supply: FSP Group Berzerker 500W 80+ Bronze Certified ATX Power Supply (£0.00)
Total: £392.74
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-03-07 13:51 GMT+0000