Upgrade priority: GPU or CPU ?

Depends on your full rig (other components) and what you demand from computer? (watching hd movies, gaming etc)
Also keep in mind that quite soon a new graphic card generation is coming and it might affect prices in whole market segment.
 
With new parts ( probably ) being released by Nvidia in a couple of months I'd opt for a CPU upgrade, it'll be held back by the GTX1050, but, then again a much faster card would be held back by the current APU.
Another reason to hold off on a GPU upgrade is pricing, over here in the UK we're just getting back to normal after what seems like a year of grossly inflated prices that may not apply where you live, though, hence this second point.
And make sure your current motherboard will accept the upgraded CPU, update the BIOS to the latest revision before making the CPU switch.
 
I'm also curious as to which I should upgrade first.
Looking to upgrade to a 1080 for GPU or 1700 for CPU, open to suggestions.

Current specs:
GPU: 290x
CPU: 8320
Ram: 8gb 2133

I mainly play Dota 2, CSGO, PUBG and R6 Siege.
Upgrading to the 1700 (with new mb, ram) is still in my price range.
 
Couple things.
1) it's not nice to hijack another's post, it gets real confusing as to whom ppl are really answering or asking questions.
2) to answer Op, depends on what you are looking to do. It's a Raven Ridge cpu, so first update the bios with latest possible. This will allow for direct plug-n-play of new Pinnacle Ridge, Ryzen+ cpus. For upgrade, I'd be looking at a 2600x but be aware, there's no igpu on Ryzen or Ryzen+ cpus. That cpu will maximize ability across the full range of games, from single thread heavy to multi-thread heavy, which your current cpu struggles with. For 1080p/60Hz, the 1050ti is fine, playable in every game, if not at max settings then at least medium or better. A 1060/6 would be an improvement but the 1070/ti is going to be the best improvement across the widest amount of games and will handle 1080p/144Hz or 1440p/60Hz monitors without much issue.

3) to answer the hijacker. You are screwed. Your platform can't handle a 1070. That FX literally does not have the IPC to push threads fast enough to make any decent use of a 1070. A 1060/6 is about as high as I'd recommend and even then won't fully utilize the gpu in quite a few games. So that big of an upgrade in gpu is wasted. In the other direction, the AM3+ platform is in no way compatible with AM4. You'd need mobo, ram, cpu. If you stuck to a lower ranked cpu such as what Op has currently, that's a decent match for the 290x, it's almost the same as an intel i5-6500. Yet you are still stuck at 4cores.

Best solution is keep playing on the old pc until you can save up enough to get a full new pc with everything you need in it, and sell off the old pc for whatever you can get for it. Do it soon while that gpu is still worth something to the cyber miners, because once that starts winding down, the market will be flooded with 290x and the gpu prices on used cards will plummet overnight.