jocey

The board has Socket 1151 and supports 6th/7th gen Intel CPUs. So you need an Intel CPU of that generation with this exact socket. The i7-4930K uses socket 2011, so it's not compatible with the board. You need an i7 6xxx or 7xxx.
 
To make sure, look at the board's specs: https://www.asus.com/Motherboards/ROG-STRIX-B250G-GAMING/specifications/
 
Then use Intel's "Ark" to get technical specs for the CPU in question: https://ark.intel.com/content/www/us/en/ark/products/77780/intel-core-i7-4930k-processor-12m-cache-up-to-3-90-ghz.html

That CPU is too old for that motherboard. Here is a list of CPUs that the motherboard supports:
https://www.asus.com/us/Motherboards/ROG-STRIX-B250G-GAMING/HelpDesk_CPU/

You are best looking at your local used market for 6/7th gen CPU's, you can't OC with that board so you don't have to go out of your way for a 'k' skew CPU, but no hard done if that is all you can find, getting an i7 6700 or 7700 would be the ideal, they still hold up for gaming.

7600k, 7700, 7700k, 6700, 6700k are going to be the CPUs you want with that board, preferably not the first though it'll suffice.
I'd go over to the Reddit Hardware Swap and try and find one there. They usually have the best deals, but you have to snag them quick.
Personally, I wouldn't be spending more than $60 on the 7600k, and no more than $120 on any of the others.

Intel's naming scheme is mostly straightforward. The first number after i3/i5/i7/i9 tells you the generation a CPU belongs to. So a Core i5 3570K would be a 3rd generation CPU, while the i9 9900K is a 9th gen CPU. In general, the higher the number, the newer the CPU.
 
As has been mentioned above you're looking for a CPU from the 6th/7th generation.
 
Do you have any idea what types of games your kid is planing on playing? Depending on this you may need to reserve a good portion of your budget for the GPU. If the games are not too demanding you might be able to get along with the CPU's integrated graphics (iGPU).

As far as i know, this board only supports up to 7th gen intel CPU. Was this board bought used? I think you can have. A cheaper and more cost efficient system going with amd right now.