The answer is a bit complicated because it depends on the games that you play and how well they are written for multi-core processors. Some properly written games run up to 50% faster with the AMD FX processors but not all. With poorly written games the full potential of the R9 280X will not be used.
The R9 280X is probably a good match for the FX-6300, IMO. I'm sure there will be online test results with the FX-6300 but you may need to wait a bit for them.
Building a reliable PC involves more than just assembling the parts. You need to be able to configure all of the BIOS settings appropriately. This can be quite involved and frustrating as it can require a lot of trial and error with stress testing. It is however often the only means to get a 100% reliable PC.