The Ryzen 3 3100 is a 4 Core 8 Thread Processor by AMD at 3.6 GHz base and 3.9 GHz boost. The Processor goes for just under £100/$100. Considering it is very similar in performance to an i7-7700 this is a very good deal. Due to recent times this processor is sometimes unavailable but when it is available it goes for a good price. This processor is all a person would need for high framerate gaming. If you were planning to stream as well as game or to edit videos or to render complex scenes then going for something like a ryzen 5 or ryzen 7 would be a good option. Also the Ryzen 3 3100 is only 65 Watts so the included cooler will be fine to use in a PC build. (The Ryzen 3 3100 Does not have built in Graphics so to display Graphics you will need a Discrete Graphics Card)

The Ryzen 5 3600 is a very good choice overall. For £160/$170 the Ryzen 5 3600 has 6 Cores and 12 Threads at 3.6 GHz base and 4.2 GHz boost and has a TDP of 65 Watts. Meaning the included cooler should work fine with the Processor. If you are looking to stream/record while gaming or do multithreaded tasks or other processor heavy workloads then this is a good choice. The reason why I chose this over the i5-10400f is because they cost the same, have very similar gaming performance (i5-10400f is around 4% better) BUT the Ryzen 5 3600 is much better for workloads outside of gaming like streaming and General usage.

The i3-9100f is a 4 Core and 4 Thread processor at 3.6 GHz that boosts to 4.2 GHz from Intel. Some people may wonder why I picked this as a recommendation and it is because the i3-9100f only costs £60/$70. This processor is ideal if your on a tight budget and but want high FPS in games. I wouldn't recommend this for streaming games or other processor heavy workloads but it will work fine with most Graphics cards for a great gaming experience. The Processor has a TDP of 65Watts so even a simple cheap cooler should be fine.