I want to start watching Lupin because I've heard it's good and it looks fun but there's so many different movies and seasons(?) I have no idea where to start. Also I don't really want to watch the very old version. I would be very grateful if someone could explain.
You can start with any season or movie (except for Red vs Green) as story arcs are pretty much independent from each other.
If you want to get more gritty and adult version (like in original manga) you can go with “The Woman Called Fujiko Mine” and its’ spin-offs - “Jigen’s Gravestone”, “Goemon’s Blood Spray”, “Fujiko’s Lie”.
You could also start with Part IV as it was intended for the new audience. Part V is less friendly. Then, there is 3D CGI movie which was good enough.
I would, however, suggest to at least try older movies (if you do not want to go through 180+ episodes of old animation), like “Castle of Cagliostro”, since that’s certified hood classic.
Parts 1-3 are completely episodic, so you can basically pick whatever episodes with a few caveats:
I strongly advocate for watching the new episodes even if you're not into the classics because not only are they worthy sequels in every possible regard, but they all stand on their own. You can watch each part independently, they tie into other very loosely so you won't miss anything, but they are more serialised, so you should start with the first and end with the last episode each. For me, each one had a different thing that was especially good about it, for Fujiko Mine it was the stylised noir atmosphere, for Part 4 it was the art and music, for Part 5 it was the story and themes, and for Part 6 it was the mystery and worldbuilding.
If you are here for the Miyazaki episodes, these are Part 1 Ep 7-23 and Part 2 Ep 145 and 155. He also famously directed the film Castle of Cagliostro.