Could be any number of things...as this is a newly assembled system, I gather. What comes to mind first is the PSU...check cabling to make sure it is attached properly. Make sure that the proper connectors are connected to the R9 390, as well. If so, next step is to install an older GPU to verify that it will work as well. None of the drivers you have used is "unstable" to the point of being able to crash your system by itself--it sounds like a hardware problem of some kind. You'll want to review the entire assembly looking for a mistake somewhere. The drivers by themselves would never do this in the absence of any hardware problems.
Check your ram settings as well in the bios to make sure they are correct (very important)--and if none of the above works you might try pulling out a single DIMM if you can.
I checked all my cables and they're hooked up correctly. However, I did notice that the fans on the GPU aren't spinning. They start spinning when I power the PC on, but stop shortly after.
I checked my RAM settings as well, nothing off there.