Lupin the Third is an interesting franchise because you can just join in at any point, they're all disconnected in terms of the stories in general, like Final Fantasy is.
While The Castle of Cagliostro is a really great film, it is light-hearted and for all-ages compared to the rest of the franchise so it might catch you off guard like it did to me when I went from Cagliostro to Mystery of Mamo.
If you like style, The Woman Called Fujiko Mine and the three films that came after (Jigen's Gravestone, Goemon's Blood Spray and Fujiko's Lie) are each pretty solid.
But out of the whole franchise I recommend starting with Lupin the Third Part 4: The Italian Adventure, because it's a great way to jump right in and pretty much rebooted the franchise for the series format, since over the decades it had mainly been annual television specials.
Worth noting that Part 4 has a unique distribution. When the series was brought over to Toonami in North America, the English dub was based on the Italian broadcast master (since the series was co-produced by Italy) which has some slight differences in timing, while the Japanese audio is based on the Japanese broadcast/BD master, so the two can't sync together and had to be on two separate releases. Both do have Blu-rays available by Anime Limited and Discotek.
The Fell Beast was the GWP.
