What GPU Should I Purchase In Order To Run Games Like BF4, And CoD Ghosts?

How many PCIe pins (6-pin and 6/8-pin) does your Power Supply provide?

Many of the GTX770's need a 6-pin AND an 8-pin PCIe connector from the Power Supply. The R9-270 might only need a single 6-pin (guessing) but then your gaming experience isn't as good.

Replace Power Supply?
If needed I can make a recommendation but expect to pay roughly $60 to $80 for something half decent.
EXAMPLE (1x6-pin, and 1x6/8-pin): http://pcpartpicker.com/part/antec-power-supply-neoeco620c

I recommend spending between $200 and $350 on a graphics card. The better the card, the better your games will look/run.

CPU and Bottlenecking:
This is going to VARY between the game, however since you already have that CPU let's ignore this. The LOWEST price card is okay, but for games like BF4 the GTX770 is going to be much better.

Examples:
$180 (R9-270): http://www.newegg.com/Product/Product.aspx?Item=N82E16814121823

$210 (R9-270X): http://www.newegg.com/Product/Product.aspx?Item=N82E16814121802

$250 (GTX760): http://www.newegg.com/Product/Product.aspx?Item=N82E16814127745

$330 (GTX770): http://www.newegg.com/Product/Product.aspx?Item=N82E16814125463

OTHER:
Always make sure to TWEAK your game (often more than once) with a SPECIFIC GOAL in mind. This is actually the MOST IMPORTANT PART as even a great system might run crappy if the settings are too high, whereas an "okay" system can run a game like BF4 nicely when tweaked properly:

Here are the two main goals:

#1: Tweak to maintain 60FPS (or 50FPS if available) 90% of the time with VSYNC ON to prevent screen tearing (VSYNC OFF while tweaking).

#2: Tweak to maintain an average of 40FPS (will get screen tearing).

Both choices have Pros and Cons. With a lower-end setup you will have to reduce the graphics to maintain a higher frame rate constantly, and it can feel a little sluggish at times (and with VSYNC ON it can actually resynch at 30FPS).

40FPS without VSYNC is something many do. If you get an NVidia card you can actually have GeForce Experience do this for you (then disable VSYNC).

Tweak:
- resolution (i.e. 1600x900 instead of 1920x1080?)
- Shadows
- anti-aliasing
- Depth of Field
- etc (find the optimal quality for YOU that hits the desired goal. Some people focus more on anti-aliasing, but remember some settings are VERY demanding for a minimal quality increase. Depth Of Field, PhysX etc might be examples of this so you can try disabling ONE feature only to see the impact on Quality and Frame Rate. Tweaking is a bit of an art.)

GAMES:
NVidia seems to have dropped the games now; I guess they're gone (was a Nov 26th date but also a Jan 31st 2014 date but no links anymore to the games).

I see no mention of AMD games either.

WAIT?
If you can't wait, these are your basic choices above. There are periodic game deals though, and you just missed a great one. It may be a while though, and STEAM always has great deals anyway so my advice is pick a card.

If you afford the GTX770, that would be my top choice (there is an Asus, MSI and an EVGA with ACX cooler as well. All great cards). I was recommending the Asus GTX770 for a time.

(It looks the the HD7xxx cards are pretty much disappearing)

The MSI has a Psu requirement of 500w, so you'll be fine. It's quite difficult to find this information, as MSI don't have it on their website but this review provides the details you need:
http://www.overclockers.com/msi-n760-tf-2gd5-oc-video-card-review
'Sounds like a cracking card, I say go for it but shame you can't get it from anyone but the tax-dodgers A****n. How about supporting another firm that specializes in PC hardware, like Newegg (if you're in the Us of course)?