If you play ds3 first you might not get some references. But that is more or less it. The story of the game itself doesn't require you to have played the other ones. I do recommend going to ds1 and 2 if you enjoyed ds3. You will have the "that's where that came from" moments.


Exactly what happened to me


I’d recommend playing in order so you can see how the games develop and change. Also some of the more fan-service stuff in the games will probably hit harder and be more Impactful if played in release order


The way the story is told allows you to play them out of order


It’s up to you. I’ve been playing since the old days and have gone in order of release for all the titles. I still remember when Sekiro was the big new game and I was so surprised at how different it was. The older you go, the more dated it is so it might be better to start old


If you're planning on eventually playing the other dark souls games, then I would just start playing them in-order. Makes more sense to start with DS1 and end with DS3, then to start with DS3 and end with DS1 imo.