AMD A8-5500 - 3.2 GHz

8GB RAM

Radeon HD 7560D - 768MB

motherboard: MSI 2AE0

those are the specs I currently have on my PC. While they arent exactly god-tier, 8gb ram and a 3.2ghz processor is enough to cut it for most games that i play. the real problem is the graphics. 768mb is barely anything these days so i need something better, and i know basically nothing about graphics cards. so to avoid blindly buying a new card, im hoping one of you guys can give me some answers. 

note: as i mentioned, i am not going for god-tier. one day in the future i can get around to that. for now, if i can get games running at medium settings at above 30 fps, i will be satisfied. also if you need any more info, just ask and im sure i can find it.

I would say a 1060 but that cpu is kinda weak tbh. It will probably bottleneck it. Also make sure to check your powersupply so that it can handle it as well as make sure you have enough space.

Lowest I would go is probably 480

Like the previous two comments said, 1060 or the 480

1060 might be overkill.
Rx470 or 480.

I would go for the 480 or 1060 as well. I'd lean towards the 1060 as it seems to do a tad better in benchmarks and a lot more games favor nVidia over AMD currently. But:

"I combined nearly 240 benchmarks across 51 games to get some real data concerning the 1060 reviews. I'm leaving for work soon, so I don't have time to go into too much detail. However here are a few of the highlights from my findings:
On average, a 1060 is 13.72% better than a 480.
On average, when using DX11, a 1060 is 15.25% better than a 480.
On average, when using DX12, a 1060 is 1.02% worse than a 480.
On average, when using Vulkan, a 1060 is 27.13% better than a 480.
AMD won in 11.36% of DX11 titles, 71.43% of DX12 titles, and 50% of Vulkan titles.
The most commonly reviewed games were AotS, Hitman, RotTR, the Division, GTA V, and the Witcher 3.
If there has been ANY bias amongst journalists, it has been in AMD's favor. Almost every single person is under the belief that AMD will get better with age. This might be true in a few years but not if we continue seeing DX11 games with DX12 features (which is the vast majority of what will be coming out in the next year or so). Essentially, the only time a 480 beats a 1060 is when AMD helps develop a title."

From https://www.reddit.com/r/nvidia/comments/4tyco0/the_truth_about_480_vs_1060/

With Microsoft releasing Xbox games on Windows 10, the 480 might be the way to go as they mostly will be directx 12 going forward.

Anything past a 970/m would do you wonders. I suggest a 1060. If you prefer AMD than the 480.

1060 is overkill. For 1080p it can max out any current game and hold 60 fps.

Your CPU would offer roughly 40% less performance than the old Intel 2500K these days.
Thought about overclocking?

If you want something cheap that will match that, the the Radeon 460 is a good fit, most MOBA's you can 60+ fps, but more demanding games you need to turn the settings down.

I'm of the opinion though that you should buy the best GPU you can afford (Provided you have a PSU that can handle it) and migrate that over to a newer platform... So I too would go for a Radeon 480.

Any game that is CPU demanding though, you will still be CPU bound, games which rely on the GPU, you will see stupidly massive gains.

I agree here. That CPU is not up to snuff. 

I think his muthaboard doesn't support the powerful GPUs since it only has a 4-pin ATX Power connector for the GPU.

So possibly you can get a Radeon 460 or a Nvidia 750, but it's important to check if they output through a 4-pin ATX and not 6-pin.

An alternative solution is to build an entirely new comp.