Depends what "family use" is. For browsing the internet and *light* gaming it will be ok, but the graphics card is on the low end of gaming cards and the power supply is underpowered and of questionable brand. Also since you're not overclocking you could save $10 on the cpu.
Are you planning to overclock this yourself? If not then you dont need k series processor, liquid cooling or z77 board. If you are then id recommend dropping the water cooling and going for a decent air cooler.
The GPU is a piece of crap, it's way underdone compared to the rest of the rig, you want to up this considerably.
With a better GPU you will need a stronger PSU.
It is fine for family use yes, but if thats all it's being used for it's too much.
I would agree with the above, but if you are set on a prebuilt, a 7850 or better and a 500watt range +/-50 from a quality manufacture like Corsair, FSP, OCZ/PC Power & Cooling, Seasonic, XFX. Closed loop water cooling is no better that good air cooling, but air is cheaper. I don't what options they give you though you but these changes shouldn't change you finaly price by much.