RadonGOG: The definite base answer to everyone who isn´t very knowledgeable on these matters is: Go highend...
...
So, buy an expensive PSU like a Dark Power Pro 11 550W or Seasonic Prime 650W (you won´t have to care about any PSU-related issues then) and an ultra-strong singleGPUGraphicsCard like a 1080 Jetstream or Phoenix. Don´t you have the money for them? Well, then you´ve got a problem.
Um... no? Why would going high-end be the "definite answer"? In fact, someone who doesn't know much about PC hardware, most likely doesn't care about perfect framerates, Ultra-HD or all the fancy visual effects.
And he doesn't have a problem if he can't afford a GTX 1080, because he doesn't really need one. Picking up a GTX 1060, as others already suggested, sounds much more reasonable.
I quote OP: "Hi All, I'm thinking of just upgrading my graphics card to give my computer
a bit more power in that department."
He's just looking for a basic upgrade, a bit more performance, not some overpowered monster PC. ( Or he'd probably have to ditch his current hardware entirely, and start from scratch. ) A GTX 1060 should easily max out ( at 1080p ) anything currently available at GOG, and is a big upgrade from his current GPU.