I recently built a machine that cost $600 total without Windows license. On a machine like that, it was RX 570 that won out. I got it for $130 and that is plenty of power for 1080p gaming.
If you go up to $1000 for the budget, I think 1660/1660 Ti makes sense if you want a rounded out machine, or 2060 if you're prioritizing gaming.
Hopefully, AMD will win back the rest of the stack with Navi. For now, the only thing they have going is price. RX 570 is the only card that I think is worth it against the Nvidia competition (1050 Ti, 1060, etc), at least until the 1650 comes out.