@IaHawk Just some random thoughts:
I agree with most here that older tech will be fine for your needs, I have 3 gamming rigs and my oldest was built in 2013/2014. It has a gtx 780ti, i5 4690k overclocked to 4.4 ghz, 8gigs of ddr3 and i just did a test with fortnight and I ave. 62 fps on ultra @ 1080p. So you could consider buying all used parts, or an entire used system. You would be surprised at some of the deep discounts you can get on entire systems as opposed to just parts. I see entire systems between $300-$600 that would fit your needs. The issue is that you are taking a risk with used, so you need to balance that with the cost.
This is gonna sound crazy but the 10th gen i3 for just about $100 is a crazy good cpu for the price. I know what your thinking, i3 is trash for gamming. Yes, I know, the old i3's were trash. I almosted just dismissed the hype about this 10th gen i3 outright but I did some sniffing around and grabbed one on sale for under $100. My buddy wanted to build a work pc on a tight budget, no gamming. When I had it in my possession I was very surprised at how good it was for the price. Its has 4 cores with hyperthreading so 8 threads and turbos up to 4.3 ghz, 6mb L3 cache, onboard video, and it runs on the newer LGA 1200 socket so you could choose to upgrade to a more powerful cpu later. It is basically the same as the older gen i5. Look, its not a powerhouse and I would not recommend this for a hard core gamming system, but for your needs (young child's computer to play fortnight), the price(around $100), and availability it may be a viable option. You could build the system around this cpu for about $500 with some bells and whistles like modular psu, NVMe drive, case with some rgb lighting (you stated your son likes this) and then go to
eBay for a used GTX 980 or something like it for maybe $150 bucks or even a lesser but still good gpu for around $100. This keeps you in your budget of $600. My simulator says you should ave. around 69 fps @1080p / Ultra settings on fortnight with this setup.
The big down side as I see it is that you would be on the intel platform and and not the AMD Ryzen platform for which I am a big fan of.
If you were willing to go to say around $700 you could go with a Ryzen 5 3600, this cpu will eat the i3 for lunch. You can build a system around this cpu for around $600 and still have all the goodies I mentioned above. Also, as long as you choose a mobo from the 500 line (B550, A520, ...) you will be able to upgrade to the newest Ryzen 5000 cpu's when and if they ever become available, they are out but never in stock. You would just need to buy a used gpu, same as above. This Ryzen system with a gtx 980 would be a formattable gamming rig for probably $700 to $750. My simulator says you should ave. around 83 fps @1080p / Ultra settings on fortnight with this setup.
If you were into spending $800 or more I would suggest to just wait for the new gen components to become available. A 5000 series Ryzen with a 3000 series GPU would be a crazy good combo if you could get your hands on either right now. The issue here is the cost of the 30xx gpu's even when they become available in numbers. Not sure what the 3060's will cost but the other cards will cost you as much as you are budgeting for the entire build. Also such cards put you in the 2k to 4k gamming arena so you will need a sick monitor as well. Probably need to spend $1500+ to get the full potential out of your components.
Good luck with your decision, would love to see what you come up with. Also, all the pricing I quote in this post is just from me fooling around on newegg for the new stuff and
eBay for the used stuff, I am sure you can do better if you actually shopped around.