KarolisLTS

should be enough for most games if you don't run too much extra stuff along with it...
it could be a good idea to get more RAM, you could use it with your new motherboard and CPU later...

Your CPU will be in the way on some more CPU demanding games...like modern open world stuff for example.
But it's still worth upgrading your graphics card you'll ba able to render higher settings while also getting much better performance. Upgrade your graphics card first...then i'd say move to 1440p monitor as your next upgrade, and then after that CPU.

You should be good in TW3, as that's an older title that I doubt will use more than 4 cores, RDR2 will be worse however, you'll probably have to tinker a little with the settings.
While the 8700K is definitely a lot better than a 6700K/7700K, it would also require a new motherboard, so there's some extra cost there as well.
If you can find a good deal for a used 6700, that'd give you a fairly significant boost in CPU intensive games and should be good for the next couple of years. 

https://www.amazon.co.uk/dp/B07598VZR8?tag=userbenchmark-21&linkCode=ogi&th=1&psc=1
Go for the 8700k, only slightly more expensive but overall a much more powerful CPU

If you upgrade your GPU, your performance is obviously only going to get better. The extent to which your CPU will be able to cope and keep up with your GPU you cannot really be sure, however an i5 6600 be able to keep up with most modern games whilst running your 1080.
 
My old gaming PC was running the i5-6600k with a gtx 970 and I could run modern games at medium-high 99% of the time, and the K version of this i5 is only a marginal improvement.
 
To put it simply, you should be fine to upgrade your GPU, but you won't feel the full benefit until you upgrade your CPU too. You will be able to run 1080p and maybe 1440p, but just tone down the CPU heavy aspects a little to compensate for the lacking of power there.
 
Best of luck

Going up to 1440p might actually be the better choice here, as it would move more of the load towards the GPU. How much the 6600 will bottleneck the 1080 though will also depend heavily on what games you play.