If you are going to upgrade the CPU get at least a Ryzen 2600!
Coming from a standpoint that I have gamed on and spent time using a Ryzen 1700x 8 core/16 thread, a Ryzen 5 1600x 6 core/12 thread, and a Ryzen 3 2200g 4 core/4 thread I will tell you straight away that the 1600 will not give you the results you are looking for. The 1600 is a good CPU and will improve your multi-tasking ability but in game isn't going to be a large change.
But like I said before you will get much more bang for the buck upgrading your video card. And as an added plus you'd have a component that could be included in a new build if you did upgrade your mobo/ram/cpu in the future.