7000 series was 1st in AM5. Next one will show up maybe in 2025?. 8000 is just 7000 with igpu changed, so they basically jump a number.
3000 then 5000(zen 3) then 7000(zen4). Next one is 9000(zen5 - 2nd in AM5).
Does not come with cooler. I use AG620 with it, but its overkill too.
Still, looking at your use case, if you really want AM5, then go for 7600(x). Its enough even for 3080 class of gpus. You can use ECO mode on those chips or set power limits yourself as needed and they will run efficiently with lower power usage and only small performance impact i think. ( So if x version happens to be cheaper by chance, can go for that )
If you have multi threaded workload ( you should know what it means else you probably dont). then only 7700 might make sense.
There isnt that much single threaded difference in performance within a generation for higher tiers to be worth it for most people. So go for 7600 rather than 7700.
If you are interested in 7700 because of gaming performance, you dont need it unless you plan to play AAA games with expensive gpus, and if so 7800x3d is going to be much better.
And 7600 will be good too. gaming performance is not too different vs 7700, like 2-3% on average and that you wont see even that with cheap gpus. Not worth it at all if you don't have another use case for it.
Ryzen 7000 CPUs have not been a slam dunk for AMD so far. Even though they are quite speedy, the move to the AM5 platform has proved...
www.techspot.com
8600 will likely be faster than both and probably faster than fastest 7000 cpu other than x3d ones. But it will likely cost near 30k at launch and then price will reduce with time if we go by past.