Opinions on my budget Gaming build? $800 to include monitor and all...

Do you need an Operating System as well? You didn't specify in your post.

And you do live close enough to a Microcenter to take advantage of their prices, right? They don't do online orders as far as I'm aware.

Is there any particular reason for going with an APU when you're going to have a GTX 760 installed? The APU works best when a lower-grade GPU is used, and if you're adding a discrete card, there's no reason for the APU (you won't get any additional benefit from anything past a HD 6670 or 6770 GPU, as far as I'm aware). The 760 beats out and 'dual graphics' APU + GPU combination on it's own.

Also, let's try a better PSU, Cooler Master isn't often considered good. And for $20, I wouldn't think I would chance a new build with that one. You don't want to skimp on the PSU- that thing dies, it could take the entire computer with it! Not to mention the fact that you say you'd like to overclock, and on a cheap power supply that's probably a bad idea. You'd be better off with something from Corsair, Seasonic, XFX, or even the Rosewill HIVE series. Keep in mind that the one you've chosen is not 80% efficient, which means it may or may not provide enough power for your system. Add to that the fact that AMD CPUs are power-hungry (in general), and you want to overclock (which means more power is needed), and... yeah.

You also don't need additional Thermal Compound, the CPU cooler comes with some that's as good or better than the Arctic Silver 5. There's also no such thing as truly 'future-proof' computers, but what we can do is use a socket that isn't going to be discontinued in usage by AMD in the near future. The FM2 socket is on it's way out, if I remember correctly. So, let's switch to an AM3+ socket CPU like the FX-6300. You may also be better off with dual sticks of ram involved, rather than a single one.

I'll just whip something up here. If you don't need the OS, just remove it from the list. Otherwise, we may need to downgrade the GPU in order to manage the budget you've got in mind, which would likely mean a 650 TI Boost. Or, you could save up a bit more and get the 760 after you've built the rest of your new PC.

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($99.99 @ Newegg)
CPU Cooler: Cooler Master Hyper 212 Plus 76.8 CFM Sleeve Bearing CPU Cooler ($19.99 @ Newegg)
Motherboard: ASRock 970 EXTREME4 ATX AM3+ Motherboard ($89.98 @ Outlet PC)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($59.98 @ Outlet PC)
Video Card: Asus GeForce GTX 760 2GB Video Card ($238.98 @ SuperBiiz)
Wireless Network Adapter: TP-Link TL-WN725N 802.11b/g/n USB 2.0 Wi-Fi Adapter ($7.99 @ Amazon)
Case: NZXT Gamma Classic (Black) ATX Mid Tower Case ($29.99 @ Amazon)
Power Supply: XFX 550W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply ($39.99 @ NCIX US)
Optical Drive: LG GH24NS95 DVD/CD Writer ($14.98 @ Outlet PC)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($90.88 @ Amazon)
Monitor: Acer G226HQLBbd 60Hz 21.5" Monitor ($117.46 @ TigerDirect)
Keyboard: Gear Head KBL5925W Wireless Standard Keyboard w/Laser Mouse ($24.99 @ Amazon)
Total: $835.20
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-09-29 01:29 EDT-0400)

The CPU should do pretty well with the games you have involved, especially once you have it overclocked. As for the Ram, many motherboards work best with dual-channel sticks of Ram, so you'd see better performance with two sticks rather than just one.

Many games use the GPU more than a CPU for their graphics capabilities. The games you've listed don't look too graphically intensive, so the combination of the CPU and the GPU should work very well. Here's what you can, in general, expect to find with what's listed here, as far as benchmarks go. The $650 build they just had the other day has the same CPU and GPU (well, maybe not the exact same GPU, but you get the idea), so this is probably what you can look forward to. http://www.tomshardware.com/reviews/build-a-pc-fx-6300-overclocking,3617.html

One thing to keep in mind is that the higher the FPS, the more fluid and less jarring the game will look. That said, getting 30-35FPS in pretty much any game should be quite good, and with that GPU, you shouldn't have an issue unless you start adding more monitors. If you want a good challenge for the build, look up the benchmarks in that review for the $650 build for Farcry 3. It's the most demanding one of the game tests, and the system does very well.

2GB of VRAM should be plenty for a while. It just depends on how quickly game developers decided to increase the requirements for a graphic card and how hard they push 'em. One thing to keep in mind is that AMD is going to be releasing their latest graphic card line-up soon: as in, within a month, if I remember correctly. Even if they don't interest you, their pricing (may) cause nVidia to react and lower the prices on their own line-up. Plus, the current gen GPUs from AMD are likely to become even more of a bargain after the details of the new line are announced.

To be honest, I have an Intel CPU in my build, so I'm not aware of a similar model to the FX-6300 that erases the problem. You could, I suppose, try a 6350, but as I said, I'm not familiar with all the AMD CPUs and such. Plus, keep in mind that that benchmark was done with a CPU with only a mild overclock due to using a standard CPU cooler from AMD. You'll be getting a better cooler from a third party, so maybe overclocking a bit further will alleviate the issue as well. Just a guess.