Everyone will recommend 2x4gb over 1x8gb because it allows you to utilize dual channel memory to effectively double the bandwidth, something that a single stick can't utilize.
If you need to cut back on money, I would rather skip the cpu cooler for now and get it later on in the future. The cpu cooler is something that you can easily add in, while a motherboard is much harder and more expensive. The Asus M5A97 R2.0 is one of the best 970 chipset motherboards.
Yeah PCPP shows a possible incompatibility, but you can probably disregard it. When Vishera processors first came out (the FX-X3XX series), motherboards required a BIOS update because they didn't initially support them. It's been quite a while since then so almost all 970 chipset motherboards should support the Vishera processors right out of the box. It's still possible to get one that doesn't support it, depending on how long the retailer has been keeping the older motherboards. I doubt they still have any in stock as it's been so long though. I have that Asus motherboard and it supported my FX-6300 right out of the box, so you should be fine.