Ok, this may get confusing, but bare with me.
That build suggested is ok. It will allow you to do some upgrades later on, but it's limited. Earlier I mentioned each motherboard socket type has a range or series of chipsets. The chipset can be determined in the motherboard model number. For example the board recommended in that build is the Asus A55BM-K. The chipset is A55. For the FM2+ socket motherboards, the A55 chipset is the low-end, A75 is mid-range and A88 is the higher-end. The chipset refers to the set of features and options (in general) as well as the quality of components used. Typically, the higher the better. So the Asus A55BM-K, while I don't doubt is a decent motherboard (Asus is an excellent brand), it is however limited in terms of features for future upgrades, even though it does have the latest socket type. I'll finish explaining this in a moment...
The CPU suggested in that build is a little on the weak side, even for a budget gaming system (in my opinion). It will work well with the R7-260X graphics card, but once you start upgrading beyond that, it may struggle a little to keep up with demand, especially when running MMO games. For only about $15 more, the Athlon X4 760K will provide significantly better performance and will be more capable at keeping up with future gaming demands. Oddly enough, I've changed my recommendation for you, but more on that later...
A quick note about motherboards and RAM. Dual channel RAM will perform better than a single stick of the same capacity. For example: 2 x 4GB sticks in dual channel will perform better than 1 x 8GB stick. Most motherboards possess only 2 DIMM (RAM) slots, meaning the total number of RAM sticks you can have installed is 2. With 2 RAM slots, this can make things a little tricky because if you want to upgrade your RAM later on, you're either forced to run 1 stick that doesn't perform as well until you're able to add a 2nd stick and run them both in dual channel, or you're forced to replace your existing dual channel sticks with new ones of higher capacity, rendering your old sticks to be kept as spares. One of the cool things about the FM2+ platform is that some motherboard manufacturers offer FM2+ boards with 4 RAM slots at a lower cost compared to other solutions.
Now, to tie all this together, here's what I would recommend based on your budget, needs and the importance of upgrade-ability. http://pcpartpicker.com/p/3gM98
Because you require an OS and monitor included in your total budget, that actually only leaves you with about $300-400 for the actual system itself. The following is a list of what I chose and why:
CPU - AMD A10-6790K - This is what AMD call an APU (Accelerated Processing Unit). It is essentially the same 4 core CPU as the Athlon X4 760K but with an integrated graphics processing unit (iGPU) that will actually deliver decent performance. This means, for the time being, you do not actually need a separate graphics card. I'll talk more about that in a moment.
Motherboard - Gigabyte GA-F2A88XM-D3H - This is really hard to beat at this price point in terms of features and value per dollar. It has 4 RAM slots so you can install dual channel RAM for better performance right from the start and simply add a 2nd dual channel RAM kit later on to double your RAM capacity without having to replace what's already installed. The A88X is the higher-end chipset, so you're getting better quality components which means it'll last longer. You'll also have the option to 2 AMD graphics cards down the road, if you so choose. It also has 8 SATA ports so you can add all the extra drives and storage you could ever want or need, as long as there's room in the case.
RAM - 8GB dual channel (2 x 4GB sticks) at 1866MHz - APUs need faster RAM to perform optimally because the iGPU uses the system RAM and typically the RAM used on video cards is much faster than system RAM. 8GB of RAM is plenty for gaming and will be for quite some time yet. When the time comes that 8GB is no longer enough, you can easily just add another 8GB dual channel 1866MHz kit (2 x 4GB sticks) in the 2 empty RAM slots for a total of 16GB.
Storage - Seagate Barracuda 7200rpm 1TB HDD - 320GB is not a lot when it comes to gaming. It will fill up fast, especially if it's your main storage drive. I was initially going to suggest a 500GB hard drive instead, but considering the price difference between that and 1TB (twice the capacity) was less than $10, it makes more sense to go with a 1TB drive. I'm using one of these in my own rig and it's a good, reliable and surprisingly fast mechanical drive that should last for many years.
Case - Your choice - I kept the Rosewill case as suggested in the previous build as it's really up to you. Just make sure it will fit a micro-ATX motherboard and you should be fine. Feel free to choose something that looks good to you but fits your budget.
PSU (Power supply) - EVGA 500W 80+ Bronze - Little bit better quality and higher wattage over the previously suggested. This will provide more than enough stable power if you want to add a fairly powerful graphics card later on.
Display (monitor) - Acer 21.5" 1080p - Little bit bigger and higher resolution. Once you add a more powerful graphics card, you'll be able to enjoy 1080p gaming as it was meant to be. With the APU alone, you will be able to run some games at 1080p but at lower settings. Alternatively you can try running them at 720p and max settings, which should look pretty decent and give you good frame rates.
Keyboard and Mouse - Up to you.
What I've basically done here is reallocated the cost of the discrete graphics card and spent a little more on certain components (motherboard, RAM, storage and display) to give you a much better starting point for future upgrades. The compromise is that initially, gaming performance will not be as good with the APU as it would be with a straight CPU + GPU(graphics card) combo, BUT - with this build, you'll be getting a decently strong CPU to begin with and the ability to throw all kinds of upgrades at this later on without having to replace anything to make it work.
Some may disagree with an APU build, but I've always thought it best to spend a little more up front on certain key components and spend less later on for better performance, rather than have to spend more later on because something is no longer compatible or doesn't support the upgrade you want to perform. Thus, if it were myself in your shoes, I would build something like this and save up to add a good mid-range graphics card in the near future. I don't know how easily you can save up money but adding a GPU in the $150-200 range and this would be a really good gaming rig that will easily out-perform the newest gaming consoles for years to come. :)
Hopefully I haven't confused you too much. There is so much to learn and consider when building a PC, especially if you're starting off with very little knowledge. I would recommend going on youtube and checkout videos by Linustechtips and Techquickie he has some great videos explaining some of the basics of PC's and PC components.