In my personal opinion, AMD's current processors are somewhat outdated and slow.
For about same price, you could get intels I3-6100 which will outperform FX-6300 in most things that don't utilize all 6 cores fully.
If you have time to wait until January, AMD's new ZEN processors should come out by then and it would make processor selection better and quite likely if it's performance rumors are true, drop Intel prices too.
Edit:
Quick search at pcpartpicker shows that for GPU, CPU, MOBO combo, 350 should be fine. There would be even space for some fine tuning.
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i3-6100 3.7GHz Dual-Core Processor (£107.99 @ Aria PC)
Motherboard: Gigabyte GA-H110M-H DDR3 Micro ATX LGA1151 Motherboard (£39.98 @ Ebuyer)
Video Card: Zotac GeForce GTX 1050 Ti 4GB Mini Video Card (£134.98 @ Ebuyer)
Total: £282.95
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-12-01 17:29 GMT+0000