Improve my rig?

If you are gaming then upgrading your CPU to Intel I5 and go with an HD 7800 or 7900.

improve performance or durability? I suggest if you wanna stick with that rig, switch the PSU into something that has 80+ certified. A god PSU will improve the durability of other components. AND that is the cheapest I can suggest to improve the rig, since you are OC-ing the cpu, you might also want a good mobo that has good VRM cooling.

Agreed. i5 or i7. If you decide to go with i5, get an 3570k (Since you OC.) If you go i7, 3770k (Also since you OC.) Also, if you go with Intel, which I recommend, you'll need to change your MB to fit it.

GPU, I like NVIDIA but AMD ones are just as good. If it's NVIDIA, GTX 680, If you have the money. AMD, 7970 or 7950, Depending on price range.

PSU you'll have to upgrade since you want to improve. More performance = More Wattage.

The main question is, What is your price range of improvements? That would help me build your PC.

Agreed with your bold statement, what is his price range? but the thing about the CHEAPEST way been bugging me...

Never cheap out when you want to OC, or in general
You get what you pay for, cheap components = trouble.

To back up what Paul Raver said I want to give an example. If you buy a crap and cheap PSU, but it provides your wattage, it could destroy all of you components that are plugged in. If the PSU isn't reliable, it will TRASH your GPU, CPU, MB, etc., and then you will need to buy almost a entire new rig. Never go cheap.

There is a difference between cheap and, lower performance but with good quality.

that's why I told him to get a good PSU

I am on Photonboy's side here. No offense but it looks like alot of Intel fan boys jumped in on this topic. The FX-6300 is a very fine CPU even for gaming. I had a similar thuban six core I recently sold and it help up very well, especially overclocked. If you want to "modernize" that, I agree with Photon. Go for the AMD-FX8350. Honestly I would recommend it over the i5 because of it's 8 core awesomeness and that more app's down the road are going to utilize them. Usually there is a sale where you can pick it up for $189 on newegg or amazon. I own it myself and it was worth EVERY penny. It's a very powerful CPU. Rips multi-threaded app's appart, runs Crysis 3 on max. If you're on a budget there is also the nearly same CPU, the FX8320 with a slightly lower clock speed, but all the same stats beside that.

Besides the Intel vs. AMD argument, you are looking are replacing your entire rig over to intel if you want to switch as your motherboard socket is not compatible with Intel. BUT... there is one minor setback here. I would bet any money you need a BIOS update on your motherboard if you want to run the FX8350. You may or may not have to, but I would definitely look into it before upgrading. But why are we talking CPU, anyway? Most of the horsepower in gaming is a good graphics card. I own the HD7950, again what PhotonBoy recommended. It's a fantastic card, especially overclocked. That one upgrade alone with your FX6300 could probably last you a good 2-3 years before needing any serious upgrades again.

bottom line:
1) Go for upgrading your graphics card, I recommend the HD7950, if you are patient and/or check ebay you can get one for as low as $250 right now, if you don't like ATI, go for a 660ti (not quiet as good as the 7950 though because of the lower bandwidth but more stable being an nvidia product)
2) If you got the bucks and care that much, the second upgrade, go for that CPU FX8350 after checking your BIOS if it's compatible, it's a fun CPU to overclock as well!
3) If you are really going to completely switch to Intel, you should wait 6-8 months as the next batch of their CPUs is expected to come out that will be better than the current Ivy bridge or whatever the current one is that's out

After some research it appears that the HD6950 is similar to an HD7850 in performance. Therefore, if you were to upgrade I recommend an HD7950 as it's enough of a jump to justify it, but the price isn't too excessive. You also have to add in the free GAMES PACKAGE.

So you're HD6950 is half decent, especially if you properly tweak your games rather than simply running on high but then getting stutter and/or low frame rates.

*If upgrading the graphics card, I recommend THIS ONE
http://www.newegg.com/Product/Product.aspx?Item=N82E16814125414

Price: $310 (after MIR)
GAMES INCLUDED (3.5 games)
1) Tomb Raider
2) Bioshock Infinite
3) Crysis 3
4) Far Cry 3 Blood Dragon (stand-alone expansion)

*I'm not sure what you can sell your HD6950 but let's assume at least $100. The games brand new are about $175 or so, but if we just use $100 (since you might buy on sale or not get all these games) then we can subtract $200 from the price of the card. After MIR etc, that should work out to roughly $150.

SUMMARY:
After much consideration, my recommendation is to buy this HD7950. After selling your HD6950 and accounting for the games the card really only costs $150 (possibly less).

I don't recommend upgrading the CPU. If you're going to upgrade relatively cheaply this is the best way I can think of. CHEERS.

UPDATE:
The MSI I recommended above has some weird comments about improperly applied thermal paste. I'm not sure if that's a big issue or not. I decided to skim comments for more cards and have come up with two different cards to recommend:

1) http://www.newegg.com/Product/Product.aspx?Item=N82E16814131458

2) http://www.newegg.com/Product/Product.aspx?Item=N82E16814202026

The Sapphire seems to be quiet and (relatively) reliable, whereas the Powercolor is also quiet but has BETTER performance than a stock HD7950.
*Seriously, read all the user reviews (10 so far) for the Powercolor card.

Other:
Dragon Age Pack is on sale for $10 at Amazon! (Dragon Age Origins complete, plus Dragon Age 2)
http://www.amazon.com/Electronic-Arts-40899on-Age-Pack7/dp/B006P28VBM

SUMMARY:
My new recommend is the PowerColor PCS+ AX7950. It has the same 4 games (3.5 really) as some other cards, is faster than stock and appears to be relatively quiet and reliable.

Why nobody pay attention to my solution? With his setup, it is already enough for gaming. It is even enough to play at 1080p with correct setting. The best answer to his CHEAPEST solution AND still categorized as an UPGRADE is to change his PSU. I believe with his setup, he needs a better PSU. Well if you do the calculation, extremely, his PSU is enough, but is it really enough to last his setup long? Considering the power supplied to each pin is different, e.g 300 watt for 8-pin for VGA, 100 watt to 4/6 pin for mobo, or something like that, and his PSU is not in the 80+ categories, I REALLY RECOMMEND him to UPGRADE ONLY HIS PSU as it is THE CHEAPEST SOLUTION there is.

sedativechunk said it himself that FX-6300 is good and even better when OC'd for gaming and to my knowledge, HD 6950 is good enough for gaming, even on 1080p with correct setting. So, the only problem is the TDP under load since he will OC his CPU and TDP of HD6950 is quite high. Bear in mind that OC-ing got something to do with altering the voltage, so you absolutely need a PSU that can supply the demand of that voltage (in my knowledge, PSU with 80+ certified all comes with good voltage regulator and not only watt that matters to be called a good PSU - read corsair blog about PSU for more information).

Bottom line, get a great PSU and optionally get yourself a decent cooling system. You are OC-ing, that's where the increase of performance came from (even for gaming, cause you can OC your VGA too). UPGRADE your PSU is a must, even your cooling system (system, not component, i mean overall, i.e for better airflow) if needed. That is the answer to your CHEAPEST solution.

Buying a new vga and procie, even new system, is total bullshit for me, since he ask for cheapest solution. Unless later he tell us that he is trolling and actually got unlimited budget.

UPDATE: to OP, since you ask wether you can improve or no improvement needed, I assumed it is your current rig. But since you didn't specify your mobo, I think this system is a mix of what you have and what you want to buy later (like CF capabilities means you want to add VGA later). If the first was the case, then I suggest you follow my advice about getting a good PSU for your already existing spec (since you state your PSU efficiency, I assume this part is already on your possession). If the later was the case, I still recommend you to buy a good PSU with the reason stated in the paragraphs above, BUT forget about the mobo with CF capabilities. Find something with good VRM cooling (like heatsink fin, heatpipe, or small fan for VRM) and good VRM. You're playing with voltage, that's what you need. Since you state "cheapest", getting a CF capabilities for adding a VGA later is nonsense. I assume it will take long for you to save up to buy another same VGA based on your "cheapest" statement, so I believe when you got the money, the availability of your VGA in the market already pretty scarce, since new series coming in just a month from NVIDIA ( I believe AMD will catch up). If getting the 2nd VGA for CF-ing is your plan and that 6950 already in your possession, then I would agree with those fanboy or some thinker here that suggesting you getting new procie or VGA or other component, sell all what you got now and upgrade it to the latest or second latest to make it last long (and CF/SLI possibility). Otherwise, stick with what you got, forget CF, do OC to get increase performance (CPU and GPU), GET A GOOD PSU to answer your upgrading question. You need it absolutely, trust me.