The r7 is a decent card. You can get one for less than $100 and it will run almost any game out there on Medium/High settings at a decent framerate. You're not going to get 60fps on Ultra in BF4 on that card.
It's not a bad card at all, it's a workhorse that will run most any game well at decent settings. Just don't expect it to run games like a Radeon HD 7970. It's a gaming level GPU, but a budget one and not high end.
Your Ram is sufficient. 4GB is the recommended amount for the game. 8GB wouldn't hurt and would provide a small performance boost, but it's not going to get you 60fps on Ultra settings with that GPU. You'd need a pretty expensive higher end GPU to get that kind of performance on a game like BF4.