I'd just start at the beginning with the Collection. Pretty sure the stories connect but even if they don't, seeing the mechanics evolve backwards or out of order can be annoying. Like you start with 4 and then when you play 2 or something and a mechanic isn't there that was nice, it kinda kills the experience. Starting from the earliest point and working up makes it feel way better as they begin to nail down and improve things.

But that's just me.

Yeah, like others have said, play them in order starting with 1. If you play them backwards or out of order, you aren't very likely to finish the first one, maybe the second, the first is kind of a slog, but worth playing. This way they just get better each time you go to the next

Played 4 first, if you do that you really notice the retrocons etc. I figure in order probably works best.

Collection > 4 > Legacy

The Nathan Drake Collection. Uncharted 1 is a bit rough around the edges, but I would recommend going in order of release either way.
Enjoy, those are wonderful games! (I might be slightly biased, Uncharted is probably my favourite video game series tbh)

Play in order of release so you can appreciate the evolution in game mechanics.

Just start from the beginning and get ready. You're in for one hell of a ride. One of the best gaming experiences out there for sure.