Don't buy a card until you check your motherboard model and power supply.
Unless you can either
(1) find your receipt with computer internals listed or
(2) contact the shop where you bought it and ask them,
you'll have to unscrew the computer case and see what's written on the motherboard and power supply. Be careful to ground yourself on the case and avoid touching the guts if you open the computer. Electrostatic damage is cumulative.
You could check if the BelArc advisor can identify your motherboard.
It was able to identify the motherboard on my older computer.
http://www.belarc.com/free_download.htmlHowever you'll still have to open up the computer to see the power supply.
4GB of video memory should be enough for the foreseeable future.
6GB wouldn't hurt but is unlikely to be necessary.
Do you want to pay more for the video card than you have to?
Maybe an extra $100 doesn't matter to you and you just feel more comfortable with extra "headroom" but it's not likely any adventure will require more than 4GB before the whole computer becomes "too old."
Are you planning to try to install the video card yourself?
If so, you'll almost certainly have to install a new power supply, and possibly also a case fan.
You will also have to reinstall video drivers.
You can use sites like GPUboss to compare video cards.
http://gpuboss.com/