you are free of course to do whatever you want with your money however if you want to get the most from your money i would advise making some good performance upgrades over anything cosmetic. cosmetic upgrades will not get you better performance in games, only solid upgades will and if you do not have much cash to work with this would be the best choice.
cable management is possible even without cable management slots and holes or without space behind motherboard trays. while not the absolute best job that can be done, you can see what i did on a small case with no real management options http://postimg.org/gallery/78slmoca/ which is more practical than pretty.
ugly components? i'd steer away from windowed cases or, if you upgraded to an i5 with another motherboard you can certainly get a black board which would work out well for both you performance wise and be aesthetically pleasing as well.
the i5 is a substantial improvment over the fx6300. while there are benchmarks such as
http://www.anandtech.com/bench/product/699?vs=1261 and
http://www.cpu-monkey.com/en/compare_cpu-intel_core_i5_4690-356-vs-amd_fx_6300-218 and other such comparisions to put it simply, the i5 is in a different class of performance. to put it bluntly even the fx8320 which is a higher tier cpu on the amd lineup is only really about i3 performance or a little better. if overclocked it can be similar to an i5 in many tasks but the i5 often wins out still. why? the i5 has stronger cores and many tasks still have better gains from strong cores over more of them. in games it is not uncommon for an i5 to have gains of 10fps with the same gpu compared to a fx8320 in such things like heavy multiplayer (32-64 player) where the cpu can start to bog down. the amd lineup can do a very good job - for the money - but in terms of raw performance intel is where its at right now.
depending on exactly how much money you have to spend would determine your options.
if you only have $100-150, just get a fx8320cpu and cooler. overclock if necessary.
if you have $280-300, get an i5-4690 and h97
if you have $300-330, get an i5-4690k and z97 (if you want to overclock that is) or go h97 with a cooler
if you have over $330, i would go with one of the i5 options above (depending on if you want to oc or not) paired with a cooler and you can push the extra money either towards a ssd ($80-100) if you want the system to feel snappy or a new case if you absolutely cant stand your current one (though its a waste of cash in my opinion).
regardless, you should attempt to get some cash for any components you are not using anymore. while you will not get anywhere near new value you can sell cpu+mobo combos and cases fairly easy if the price is right and the components work. this would help offset the cost of your upgrade. a good rule of thumb is take 15-20% off new price for every 6months of age and start there (though sometimes you need to adjust this number a bit up or down depending on demand of parts).
again, your choice but i think for a limited budget you should focus more on performance than aesthetics. (for the record, some of the h97/z97 boards are black and look rather nice.