Well WoW, LoL, and even GW2 aren't massively demanding. BF4 on the other hand, is among the most demanding games out there now.
I still don't fully know what it is you need, as I think there are a couple of things you are missing.
Firstly, do you want to play games across two monitors (ie stretched across, or multiple clients) or are you just looking to play on one, but have a second running at the same time (for web browsing or whatever)?
Secondly, the size (dimensions) of your screen(s) are irrelevant, but their resolution (or the resolution you want to play at) is not. Resolution the number of pixels your graphics card needs to fill in, so makes a huge difference.
As for compatibility, you have no issues. Your motherboard is PCIe 2.0, and most graphics cards these days are PCIe 3.0. The systems are backwards compatible, PCIe 3.0 just has a larger bandwidth to cover future development. Right now, it isn't going to cause any limitations. As for installation, its very straightforward; drop the card into the slot, it should click, one screw locks it in place. Then it's just a case of connecting the PSU cables.
As for the R9 280X, you are right it is very competitively priced, and could well be the card to go for. For a single 1080P display, it's very very strong. As BF4 is potentially the game that's going to cause you most problems, I'll focus on that. Assuming a 1080P display, and more or less maximum settings, you can hope to achieve somewhere in the ballpark of 50fps with a single monitor and it would drop under 30fps with a second added. Obviously you can tweak settings to boost performance accordingly and get things to a comfortable level.
If you want to run at higher resolutions than that, or want to enable the supersampling setting, then you realistically need to spend more money to get a decent performance level.
In terms of alternatives, at that level you have three cards, the R9 280X, HD7970Ghz and the GTX770. The 280X and 7970 are very similar, as they are internally the same thing, with some small changes. The 280X is going to take over entirely, but if you are looking for a bargain then its quite possible you'll see heavily discounted HD7970s popping up from time to time as they try to clear stock. The GTX770 offers similar performance and if you have a preference towards Nvidia, then the price gap really isn't that big, but if it were my money I was putting down, then I too would be very tempted by the Gigabyte 280X.
As for PSUs, the HX750 is a decent quality unit but 750W seems like a slightly pointless amount in this case. If you have an intention of going for Crossfire 280X at some point, then it isn't really sufficient to support that, so it's not really helping you. Given its current price, it's a pretty good buy, but if it changes, I'd be flexible and shop around. In the next week or so there will be a lot of good deals.