LGA1151 is actually too vague to say. 6th and 7th gen stand apart from 8th and 9th gen. Same socket, different pin layout and they are not cross compatible. But if is is Z170 or Z270, then the i7-7700k is the best you can do. Z370 or Z390 and you can go for the i9-9900k, i7-9700k, or i7-8700k (my choice would be the i7-8700k for cost/performance) That includes the lesser chipsets as well, though I think your six+ core friends won't like living too much on B series boards. H would be okay.
Quad core with hyperthreading is quite a step up above the average gamer. The i5-4460 you have now is still a little above the curve. Keep in mind that the vast majority of PC gamers run off the shelf PCs and laptops. Game developers will target them as much as they can. So dual cores are just now finding themselves in a bit of trouble. Dual cores with hyperthreading, still viable. Brand new machines with Ryzen 2200G (only a quad core) still viable, even with the onboard graphics only. Not going to win any performance contests, but in terms of playability a quad core is still good enough.
I have an i7-7700k and a GTX1080. Pretty much the fastest consumer chip when the 1080 was first available (Though I think it was i7-6700k at the time, I ran my 1080 with my old i7-4770k for several months only upgraded so I could have an NVMe drive). Difference between those two chips was about 20% maximum performance on CPU only. But the CPU is not maxed out when I run it, but I am also running at 2560x1440. My GPU is the limit there.
You could do the same thing. Go for a higher resolution monitor and let your GPU set the pace. If you target high frame rates you need both CPU and GPU for the best results.
An i7-4790 or i7-4790k would be a more economical upgrade for you. The alternative is needing new DDR4 memory, which is still somewhat pricey. A new motherboard, and processor. Along with the new GPU, and a monitor, and you have pretty much built a new computer.
Ryzen is a great option, but not for maximum FPS. Again, at higher resolutions it doesn't matter so much what CPU you have. But if you want to stay at 1080p then you'll want as much CPU as you can get.
Were I building today, i7-8700k or i7-9700k would be my choice. Probably the i7-8700k from what I have read about 9th gen so far (runs a little warm despite having solder, would rather de-lid a pasted CPU than a soldered one if I had to) A goodly amount of DDR4-3200, 2x8GB. And a nice Z370 or Z390 motherboard.
Ryzen, would be the R5-2600 (currently $249.99, which is a good bargain) and a nice cooler, fastest memory I could get, maybe 3466 if it would run. X470 motherboard and shooting for absolute maximum overclocks.. 4.2Ghz would be reasonable. It would still lag 20-30 FPS behind a comparable Intel chip though, that extra 500Mhz or so really makes a difference in the FPS game.