at $300, 2060 is best but you might be able to buy 5700s for like $330~340, that is like 10 percent better depending on the game but you are losing nvidia features like vrs, rtx etc and AMD drivers for 5700 are pretty sketchy right now. It's up to the individual if they care about that delta or cost difference. Both are good cards for the price.
For $200? Every thing out there is mediocre, outdated and not worth buying imo. We are looking at cards like 5500xt, 1650 super, rx 580, 1660 (not super or Ti) etc. They are all about same and I just dont think it is worthwhile to buy into that kind of performance in 2020 unless you can find a used rx 580 or 570 for really cheap. If you want to buy new, I would go for 1660, it is generally the fastest one and has 6GB VRAM which is a lot better than 4.
If you move up to $250, you have 1660Super which is alright and appreciably better than those cards but still feels like you are paying too much when you can pay a little bit more and buy a RTX 2060 which is a pretty decent step up in performance and features. Overall this market sector sucks right now. You have a lot of mediocre or not so great options and there is no clear cut choice whatsoever. Personally, I would not buy anything below 1660 Super, I think they will become obsolete soon and I expect more from a $200 card. 1060 GTX or RX 480 were ~$200 card but they offered amazing performance three years ago, we just haven't advanced much at all. Just watch this video to get an idea how poor of a value these cards are right now:
https://www.youtube.com/watch?v=lgt5xiFWDlc