What is the best possible mostly gaming PC I can get with around $1200-$1250?

Methodz

I already have the monitor, keyboard, and mouse. I would also like the build to include Windows 10. Thanks!

C0v3rt_X

If you want to go all out, Go team blue (Intel). AMD will save you some money BUT for pure gaming and some professional work, Intel is the way to go.

TSTonyV

I'm actually going to slightly disagree with C0v3rt. While Intel does generally have better in-game FPS in equivalent scenarios, depending on your budget AMD may be the better option because you may be able to get a better GPU with the money saved on the CPU and a less expensive motherboard. In your case, I think that scenario applies very well. I came up with two different builds, one Intel based one AMD based, for comparison:

AMD: https://www.microcenter.com/site/content/custom-pc-builder.aspx?load=f92f2ed5-c851-4c60-ab4c-a331caae99eb

Intel: https://www.microcenter.com/site/content/custom-pc-builder.aspx?load=6895a209-71be-4a2f-9b54-0bcf09a00e68

All the parts I selected are identical, except for the CPU and motherboard. The i5-10400 is the closest direct competitor to the Ryzen 5 3600 in terms of performance, and they're very similar in general. However, on the Intel build due to the added cost for the motherboard and CPU, you have to downgrade your GPU in order to stay within the budget you selected, which in most situations means your gaming performance won't be as good.