What Should I Upgrade First?

Solution
You said it's getting slow recently, have you cleaned it out recently to blow dust out of the pc? Have you tried using amd overdrive to monitor cpu temps (thermal margin, overdrive show how many degrees until throttling point reached rather than running temp). The motherboard isn't the greatest for an 8 core fx like the 8350, it's only a 4+1 power phase board and the vrm don't have heatsinks so more prone to overheating while trying to power that cpu.

Are you using the standard/stock cooler or an aftermarket cooler? Stock coolers or coolers that blow down against the motherboard are important especially for vrm that have no heatsinks. Something like a 212evo or liquid cooler that don't blow across the vrm can make the problem worse...
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ok so your video card isn't really worth upgrading, it's probably less than a year old and there isn't really any point.

But the reason I see your computer is lagging, is the processor. You might not like to hear this, but the fx processors are getting a little old, and definitely have served the community well.

At this point, you might want to wait for intel to release coffee lake, so yea

If you don't wanna wait, I suggest a mid range i5 to go with your 1060

But upgrading the processor means you have to upgrade the motherboard as well, so you could try B250, and however much ram you want (8GB is the norm these days)
 
You said it's getting slow recently, have you cleaned it out recently to blow dust out of the pc? Have you tried using amd overdrive to monitor cpu temps (thermal margin, overdrive show how many degrees until throttling point reached rather than running temp). The motherboard isn't the greatest for an 8 core fx like the 8350, it's only a 4+1 power phase board and the vrm don't have heatsinks so more prone to overheating while trying to power that cpu.

Are you using the standard/stock cooler or an aftermarket cooler? Stock coolers or coolers that blow down against the motherboard are important especially for vrm that have no heatsinks. Something like a 212evo or liquid cooler that don't blow across the vrm can make the problem worse.

If you're interested in upgrading regardless, either intel or amd have decent options now. Consider kabylake (7th gen intel) or amd ryzen. Not sure which os you're running but keep in mind the most recent cpu's from intel and amd both are designed to run with win10 and neither are officially supported on win7 or 8/8.1.

You'd be looking at cpu, motherboard, ddr4 ram, potentially an aftermarket cooler depending which cpu you decide on along with a reinstall of windows. If your psu is somewhat older, 4-5yrs, you may want to consider updating that as well.
 
Solution
You say your PC is getting pretty slow,did you try installing new OS?
I you really want to upgrade,buying a new motherboard,wouldn't be a bad idea.
Or you could buy a cooler for your CPU,FX series tendes to go really hot.