Free-Sync is great tech so stick with it, i'm looking at switching to AMD because of it, Nvidia's equivalent is no better and WAY too expensive.
The really unfortunate thing is not just that this has happened but also at this time, GPU's are transitioning to new tech, AMD's 480 is a really good card but only available in
reference design
Older GPU such as the 390 are being phased out of sales, AMD don't make them anymore, the good news is they are cheap and still great cards, nothing at all wrong with them and
this one i pointed to is a good one, if you can't wait thats what i think you should get.
There is also
this for 10% more than your budget, they are about 20-30% more powerful than the 390, IMO overkill for 1080P but its another option, i also think your PSU 'while it should be ok' will be more stressed by it.
Or if you don't mind a reference card (can be a little noisy) then get
this one, its the cheapest 480 Reference which is the best policy as they are all exactly the same and all made by AMD.