1. My case is this: http://images.getprice.com.au/products/BimgAcerAspireM3970.jpg
2. I will need to buy a new PSU. My current PSU is 300w. I think I will need 600w.
Assuming a modern i5/i7 Haswell, you're normal max in gaming should be under 400W.
You might as well get a quality 600W though since it's ideal to keep the load low, and the fan won't be as loud. Here's one example:http://pcpartpicker.com/part/evga-power-supply-120g10650xr
(You'll have to manually measure what LENGTH of card is supported unless you can find that info online)