is my rig going to cut it?

[skanob]

Try this:
PCPartPicker part list
CPU: Intel Core i5-4570 3.2GHz Quad-Core Processor ($189.99 @ Newegg)
Motherboard: MSI B85-G41 PC Mate ATX LGA1150 Motherboard ($79.49 @ Amazon)
Memory: G.Skill 6GB (3 x 2GB) DDR3-1600 Memory ($66.99 @ Newegg)
Total: $336.47

you just need to worry about your case, power supply, and storage.

(I'm starting to get an idea of the builds "necessary" for Dolphin)