As a point of reference what CPU is in the system now?
The reason is if a game is predominantly single threaded, then you'd see some performance increase with newer generations of CPU. Within the same generation there may be some but usually not a huge discrepancy. However, if the game is well coded for using multiple threads and you have an i5, then an upgrade to an i7 would prove more beneficial. Keep this in mind.
As mentioned I don't believe the generic RAM would be an issue for an Intel system, and perhaps would be fine with the Ryzen 2x00 series CPUs. From what I can tell, it should be DDR4 RAM. I would suggest using something like HWiNFO to get the information.
So now it depends on how you want to upgrade. Do you go the minimalist new build (low end build but with current generation components) with an eye on a further upgrade on the same motherboard? Or perhaps the best you can afford build?
I would say that an upgrade to an i7-6700 isn't necessarily a bad one. People have held onto their i7-2600k for many years before Intel's 8th and 9th generation CPUs actually offered something truly better. I would consider the cost of an i7-6700 to the cost of a new platform to see how cost effective it can be. By all means start a new thread with a budget and stating your requirements, and I'm sure a resident builder can make some good recommendations.
Another factor is the Windows licence for your current PC, being a prebuilt, likely means it is connected to the motherboard. Standard knowledge would suggest such OEM licences cannot be transferred to a new motherboard. However, one mod here has noted that as long as the licence is digitally attached to an MS account, it should work without the need of a new licence.