13600KF for $250 on Amazon right now seems like a nice deal unless you need 14th gen
could get away with a 12600KF with a 4070 but I think it's worth paying more for the raptor lake cores. alder lake is gonna struggle a bit with 1% lows by comparison
noctua U12A works well and is nice if you prefer a smaller form factor air cooler that doesn't cover your ram
i use the dark rock elite and it's been wonderful
a 280-360mm AIO will help you maximize your performance but for me it's not worth the extra hassle and risk associated with AIOs.
keep in mind your bios settings may be optimized for water cooling out of the box, depending on your motherboard. for my msi board, i just had to go into cpu settings in bios and change water cooling (unlimited power) to air cooling (288W power limit) in order to get my fan curves dialed in
had a U12A on my 12900K for a while actually. thermals were fine but the fan noise can be a bit much at higher RPMs. that will come up in gaming unless you set a custom fan curve or power limit the proc. tried fan curve first and it gutted my R23 but ymmv. simple power limit of 250W was good for 90-95% of liquid-cooled performance in my limited testing.