A GTX 1060 is a better value, it should be plenty for 1080p gaming at high settings, and the price difference is not that big.
Too bad Black Friday/Cyber Monday is over. They had some pretty decent deals on cheap computers/parts.
You get more for your money if you build it yourself. It's really not hard, it's mostly just a matter of putting together pieces where they fit. And it's a lot of fun too. And you could get help here with putting together the parts list.
As a starting point, there's this generator that puts together a parts list based on a budget that's supposed to pick parts that give the best value for money within your budget:
https://choosemypc.net/build/?budget=600&oc=false&options=
At $600 it suggests an i3 with a RX 480 (and SSD+HDD). At that price, that's probably about the best you're going to get, though it might be worth it going with Ryzen instead. And if you already have a HDD you can reuse, you can get a bigger SSD instead.
Don't get an all-in-one. You get less for your money and upgradability is poor. It has the same drawbacks as a laptop but without the portability. At that point you might as well get a laptop.