Lupin the 3rd is one of the oldest names in anime/manga. The basic story, of one of the worlds most renound thieves has been in production as a manga, anime or even live action movie since the late 60's.
This begs the question, Where do I start?
Simple, it is episodic. So much so, that you could catch almost any of the movies, TV series or manga chapters and hardly be out of touch with what is going on. In the history of how I first saw Lupin and his merry gang, I rented Castle of Cagliostro on VHS at a video store in the 90's.
I had no problem figuring out that Lupin was a thief, a good one. He had a rather loyal if not beatnic looking partner named Jigen and a sometimes extra partner in the form of a hired Samurai named Goemon.
I also quickly learned Lupin had a rival/love intrest in the form of the full figured Fujiko and a comic nemesis in the form of the always trench coat wearing, ICPO cop, Zenigata.
Anyhow, the movies in my opinion are a good way to go, but that does not mean you could not just start with one of the TV series. Expect comedy/unbelievable events/ and action.
*Edit, 1 movie that might be good to have at least seen Lupin in some other form, is Green Vs Red. And Fujiko Mine, is an interesting title, because it comes at the franchise in a whole new way, it follows the main female Fujiko Mine, and offers a version of how the group met.