Run a free app called CPU-Z.
It will identify the processor you now have.
It is unlikely that there is any processor significantly stronger than what you have, but you never know.
As a guess, such a pc might have come with a Athlon X4-465 processor.
It has 4 threads and a passmark performance rating of 2212. It has a single thread rating of 1243.
The single thread performance is usually the most important performance metric for games.
There are other processors, but they will be 125w processors which your motherboard can't handle.
https://www.cpubenchmark.net/cpu.php?cpu=AMD+Athlon+II+X4+645&id=174
The strongest processor upgrade might be the 6 thread Phenom X6 1065T.
It has a rating of 3239/1341. A small upgrade, but probably not worth the $65 or so it commands used on ebay.
GT710 is not a gaming graphics card. It has a passmark performance rating of 638.
Spend a few bucks and build a starter gaming pc with your son.
A $115 i3-10100 has 6 threads and a rating of 9021/2561.
https://www.newegg.com/p/pl?N=100007671 601351801&Order=1
It includes HD630 integrated graphics with a rating of 1167. Not considered great for fast action, but really not bad.
Any lga1200 MATX motherboard will do.
Here is one for $60:
https://www.newegg.com/p/N82E16813157931?&quicklink=true
You will need ddr4 ram.
Here is a 2 x 8gb ddr4 2666 speed kit for $55.
https://www.newegg.com/g-skill-16gb-288-pin-ddr4-sdram/p/N82E16820232718?&quicklink=true
Power requirements will be minimum. 300w will do.
Likely, you could use the one in your HP pc.
You probably could use whatever HDD came with the pc.
But,
I will never again build without a ssd for the "C" drive. It makes everything you do much quicker.
240gb is minimum, it will hold the os and a handful of games.
If you can go 500gb you may never need a hard drive.
With ssd prices down, even 1tb is reasonable.
There are cheaper ssd's, but samsung is top quality and performs better.
A 250gb samsung 860 will be $50, 500gb is $70
https://www.newegg.com/samsung-860-evo-series-250gb/p/N82E16820147676?&quicklink=true
This is for starters.
In time, kid will no doubt want to install a strong discrete graphics card for fast action gaming.
Perhaps something as strong as a GTX1660 super, a $170 card.
That will be limited only by the power supply capability.
Here is a chart of gpu options:
http://www.realhardtechx.com/index_archivos/Page362.htm