I'm stuck between the Intel Core i5-9600KF and AMD Ryzen 5 3600
Looking something that will last a good few years for the first person shooter type gamer.
Do you mean the cpu itself last? or the whole system built around the CPU makes a good foundation for future upgrades so it will last?
As far as the CPU, that's hard to say any will last as no one knows what the future holds as both gaming demands on the CPU, as well as the things you can do while gaming that put greater demands on the CPU, can each limit useful life. We just don't know what may come, no one has a crystal ball, that's just one reason there's really no such thing as 'future proofing'.
It used to be the best way to get an easy upgrade path was going Ryzen, but with AMD shying away from upgrades on the same socket even that's a bit dicey just how far you'll be able to upgrade some AM4 systems now. But choose wisely, you could get at least one more generation of CPU in the same motherboard you put that 3600 on. That would mean getting an X570 board, or B550 if you can wait a while.
So in the right motherboard a 3600 processor will pair well all the way up to a 2080ti to play any current game very well even at 4K and 1) upgrade to CPU's with way more cores/threads (all the way up to 16core/32thread currently) to help with doing things alongside the gaming as you get the urge to do it and 2)allow you to upgrade to a Zen3 CPU and move into the next- gen Ryzen architecture. How far into the future that might get you is anybody's guess.