I'd say 4gb vram is 'enough' to both play and enjoy most games, assuming the rest of your system can keep up. If you're new to PC gaming then I want to advise you that just adding a fast videocard doesn't solve all performance problems. Some games also need a certain amount of CPU power. Some games can have performance issues due to poor optimization of the game itself, no matter what CPU and videocard you have.
Day Z minimum says an Intel i5 or equivalent, and a 2gb gaming videocard are suggested. Arma 3 is an older game so you should be able to run it with less. Arma 3 had a reputation as not being optimized well, I don't know if that's still true.
An Athlon dual core, even if it's an Athlon II, is not 'average' these days. It's very low performance. You might need to stick to less demanding games if that is what you have. Your motherboard will determine how much system ram you can use, and you'll need a 64 bit version of Windows to make use of more than 4gb system ram.