Honestly open to suggestions.  Intel seems to be the way to go.

How difficult is overclocking?  Might be a bit beyond a first time builder?

not too bad and honestly you really don't need to overclock as long as you get a good Intel CPU. Its helpful to overclock if your pushing your rig to its limits but for most general gaming you won't need to overclock at all. Are you looking at AMD GPUs or Nvidia?

Building a PC is really easy so you shouldn't be too worried about that. The first time I did it I watched this video while doing it since I was pretty nervous.
http://www.youtube.com/watch?v=d_56kyib-Ls

Anyway for a gaming PC, since you are on a budget don't spend too much on the processor. It will almost never be the bottleneck in modern games.

I play most of my games on ultra on a 1080p screen and can even play battlefield 3 and dirt 3 across three 1080p screens on ultra with this computer.
Radeon 7850
Athlon II x3 450 processor
8 gigs of Ram
Some generic shitty AsRock motherboard
Cooler Master 500Watt power supply
I build this computer a while ago and only upgraded the graphics card so far and I only had a $400 budget when I built it. So you could do a lot better.

From the website you posted with your budget I would probably go with the following.

AM3+ x6 FX-6300 $145 (CPU)
WD Black SATA3 1TB $92  (HardDrive)
AsRock 970-Pro3 $89 (Motherboard)
2G R9-270X Sapphire-OC $229 (GPU)
8G Kit 1600 Patriot-S $89 (RAM)
Antec HCG-Modular620M $125 (Power Supply)
SATA DVD RW LG $19 (Optic Drive)

And whatever case you like. Just makesure it isn't too small for the motherboard though thats pretty unlikely.

Total price will be around $840, excluding a windows license. 
If you prefer Nvidia I would go with the 2G GTX 760 Gigabyte OC for $314. But your total price would become a little out of your price range.

I might skip overclocking this time around, go with some extra wattage as you suggest, and look into overclocking on a second go some day.

Again entirely open to GPU suggestions, in hand with comparable CPUs and motherboards.

Thanks a lot for your suggestions.  What does everyone else think of this potential build?

I can be a bit flexible on the price, I am more concerned about compatibility/not making a complete twat of myself and fucking the whole thing up.

Do you want to get a SSD (Solid State Drive), or a 7200RPM for the Boot Drive?

Solid State Drives are much faster at reading data than mechanical hard drives are, but are more expensive per GB.

Most people including myself usually have a small SSD drive as the boot drive (this is the drive your O.S. is on) and another hard drive for extra data storage.

Lastly, adding the cost for Windows 7 or 8, usually adds another ~$100 to the cost of a PC, is that also a cost in your build?

The main issue with compatibility is making sure the processor and motherboard are compatible with one another. For amd the newest processors have AM3+ in their name so you just pick a motherboard compatible with AM3+. The other things you might want to check for the motherboard is how many RAM Slots it has and what the maximum frequency of the RAM can be. You can find all this info about the motherboard by just googling the part and clicking the manufacture's link.

RAM frequency is just the number next to the RAM. So if you get 1600 RAM you would want to get a motherboard that is compatible with 1600 or higher RAM to take advantage of the extra speed. Personally I would only get motherboards with 4 RAM slots so you have room to upgrade in the future.

Intel is a little more confusing, but a lot of people prefer intel systems to AMD. If you decide to go intel just google the processor you pick.
I would suggest the Intel i3-4130. Click the manufacturer's link and look at the socket type.
http://ark.intel.com/products/77480/Intel-Core-i3-4130-Processor-3M-Cache-3_40-GHz
For this processor it says 

So you want to get a 1150pin motherboard.

Again this is entirely personal opinion but I would go Nvidia over AMD. Don't get me wrong AMD has some fantastic cards but to me Nvidia are the best. The best card close to your price range is probably the 760, though if you could scrape up a little extra cash and get a 770 you would in no way regret it.

Happy to include an SDD if it increases overall performance without devastating the cost.

I am not including Windows in the cost, I know I'll need to pay extra for that.

Cool, which motherboard/CPU should I put with those cards?