You can still use AMD. I use an FX-8150 and play The Witcher 3 without any issues, that said, AMD has majorly stumbled with their more recent CPU's. AMD's Zen could be good, but I would recommend the Intel Skylake CPU's if you are going to be swapping out the motherboard. But, these processors won't be out until August.
You can upgrade this PC, but you are limited in terms of the CPU. About the highest-end processor you can get with that motherboard is AMD A10-7800. This is not as powerful as the FX processors, so you may want to do a rebuild of this PC with more powerful components.
If you cannot wait a month or two for Skylake, you can try the following...
Motherboard: GIGABYTE GA-Z97-HD3
CPU: Intel Core i5-4690K Devil's Canyon Quad-Core 3.5GHz
OS: Windows 8.1 (You cannot transfer your old Windows license unless it is a full retail version and not an OEM/System Builder copy)
GPU: EVGA 04G-P4-2974-KR GeForce GTX 970 (Make sure you already have at least a 500W power supply)
You can keep your RAM, optical drive, case (Assuming it isn't a custom or slimline one), and hard drives. You should be below the $800 mark. If you would like to splurge, you can get an SSD such as the Crucial BX100 CT250BX100SSD1 2.5" 250GB for your operating system and most frequently used programs.