Buildapc

Obviously very dependent on where you are and other factors, but in that budget I would try to find a company throwing out/giving away old office PCs, get one of those for free or as cheap as possible, and sticking something like a RTX3050, RTX5050, or RX6600 in it.

It kinda depends on what you want to do with it but it'd be better to get a a secondhand pc somewhere for office use with like an i5 or i7 from recent times and try to fit a small recent GPU in there. The specs you are giving will maybe run some very basic games at 1080p60 but will be completely obsolete in less than 2 years.

It might even be better bang for buck to get an Xbox Series S at this point, you can hook up keyboards and mice to it.

The rx560 is pretty long in the tooth at this point and was a budget card when it released about a decade ago. That build isn't far off from my wife's PC before I rebuilt it last year (4th Gen i5, 12GB of DDR3 and an RX560) and it was pretty well rounded in everything being a bottleneck. Like she played plenty of games at 720p on it, but it wasn't fantastic. Took a lot of settings tuning in every game to get things looking decent and performing well enough

It sounds like you're building a PC for a friend or relative, I would steer them towards either a used console or encourage building a system without a discrete GPU and encourage them to circle back in a few months to a year and see if they can scrape together the budget for an RX4/580 or a used 20/30 series Nvidia card. The fact is, at that price range a bit more money can net you a lot more performance, so waiting and saving a little more is going to be the better option if possible