In this instance it is more about pairing your hardware with equally performing components, IE. GPU + CPU. An A8 6/7K is a fairly weak quad core CPU so you would not want to pair it with say a GTX 960/R7 370 or above. Any slower GPU than those will be fine as they will be supplied with data by your CPU at the rate they demand. 

When the GPU is significantly more powerful than the system can handle it ends up being starved for data. The result is high CPU usage and low GPU usage, if it is the other way around the reverse is true. The ideal is to have both CPU and GPU both running at or near 80% in any given game. If both are running higher than 90% in a game then lowering settings will likely produce smoother gameplay. This is only a rule of thumb however and many games will spike even the best hardware to 100% usage on one or both CPU/GPU at times due to poor optimization etc.

If you want to know more than this take a look at the subject via google. I would search "PC Bottleneck information".

"For a decent gamer on a budget using as much of your current system as possible".

With that hardware config there shouldn't be any bottlenecks as the GPU will run out of horsepower before the A8 starts bottlenecking the system. It comes down to quality settings and resolution being tailored to the hardware. The goal should always be an enjoyable playing experience so better to have a game set to 720p medium settings at 45 - 50fps than to have it set to 1080p low at 25 - 30 for example.

If you should choose to upgrade your system at a later date (and have the budget for it) then you would do well to wait for AMD's Zen lineup to be launched. Regardless of which CPU you would go with, intel or AMD, the launch of Zen will hopefully present competition for intel and force intel's mid range pricing to be more competitive.

If you are not looking to replace everything then the info I provided above should do you well. You may even consider going for an Athlon x4 860, it is a faster CPU than the A8 and costs about the same. You can only do this if you purchase a discrete GPU however as the Athlon FM2+ CPUs do not have built in graphics. That wouldn't be a problem with the GTX 750/Ti.

For a decent gamer on a budget I would recommend the following:

4 Core CPU (A8 is fine in your case though I would try and get an A8 7k series)

GTX 750/750Ti with 2gb of memory

8GB of RAM

This should allow you to play most AAA titles at decent FPS @720p (even 1080p in some titles) with a mix of low/medium and sometimes even high quality settings. You will have to tweak your visual settings for optimum quality vs FPS but most games today actually look pretty decent even with lower settings.  Google search the combination of APU and GPU you plan to get and take a look at youtube videos of gameplay with the combo. 

The parts I listed above will be night and day compared to the APU you are using now