Rexx

As long as its a good PSU you should be ok. As far as the 3600, I say go for it unless you feel it's time to upgrade. 

There may be some slight bottlenecking on CPU heavy games but you should be alright. How many watts is your PSU?

https://www.tomshardware.com/features/nvidia-geforce-rtx-3080-ampere-cpu-scaling-benchmarks
 
TLDR it's a 30% bottleneck at 1080p, 15% at 1440p  5% at 4k, doesn't mean u wont benefit from the gpu upgrade though., the 3080 is beast.
 
it also depends on what refresh rate ur monitor is.

COD MW can probably handle medium/high on a 2070 no problem.
 
monitor recommendations really depend on your budget, because you can get different panel types and sizes and all that.

144Hz is the sweetspot since most AAA games wont run above 200fps due to cpu limitations
but if you can get 240Hz with g-sync(compatible) that isnt priced too different, then that's good too

Start with the GPU you already have and if the games you are playing aren't doing well at the graphics settings you prefer, upgrade then.
 
What games do you play most, and at what settings?

Your 2070 will do just fine. Obviously not all games at max settings but most games will run above 100FPS at 1440p if you tweak the settings.