I would say 8GB or RAM was a minimum these days, even with an SSD to swap to. If the machine seems to be stuttering, then that is an obvious and fairly cheap thing to fix specially if you have spare ram slots on the motherboard. That won't help the maximum frame rate, but would make the machine more pleasant to use.
The GPU is the next obvious thing. That is purely down to what you can afford. You can get a RX 460 for £90, and although some people will slate a 2GB graphics card at this low end at 1080p it shouldn't be an issue. Benchmarks are often at Ultra settings, and you don't want to be using those anyway. If you can afford it, the RX 470 can be had for about £180, I would much rather spend the money there than mess about with the CPU.
Mind you, once you look at the RX470 you are on the slippery slope to a
http://www.ebuyer.com/753965-gigabyt...0g1-gaming-4gd
Edit: What power supply do you have? Power rating, any PCIe or Molex 4 pin connectors available on it?
Another edit:
https://arstechnica.co.uk/gadgets/20...aphics-card/2/