Is this a good build?

I would go with the new A10 over the older A8. You'll get much better graphics performance as well as more core performance.

The website says the A10 is not compatible. Why is it not?

Because you need an FM2 motherboard to support it.

If you want to have an AMD build I would go with this
http://pcpartpicker.com/p/oGNX

An Intel build would cost more but have better performance
http://pcpartpicker.com/p/oGWa

Don't forget an operating system, Windows will add another $90 to the build.

I would change the case out of the second one, but it looks alright.

IS that for just looks or is there any reason?

Well, InWin doesnt make fantastic stuff.

Id definitely go with an A10 too

other thing to note is that the case you have includes a cheap 300 watt power supply , and you have also included another power supply

Perhaps that is deliberate . I doubt the inwim case is good quality anyway , and white cases look silly with black monitors/keyboards etc IMO

With either the A8 or A10 builds I'd pay a little more for a Kingston HyperX lovo 1.35 volt 1600 MHz kit of RAM . Set manually to 1.5 volts it will run at1866 MHz and improve graphics performance