One of the many annual TV specials, First Contact offers one potential origin story (told by an unreliable narrator) about how everyone got all tangled up together in New York City. With Zenigata as a Japanese cop on the Fujiko Mine case, Goemon out in Japan, and Jigen as a bodyguard hired to protect a treasure the phantom thief Lupin III has his eye on, it's interesting to see a different side of these characters as they interact and actualize into the gang we know and love. The grimy look of the city is aided by the less-saturated style of early digipaint shading for the animation, and the city is given plenty of texture through detailed matte paintings.
This is a happy medium between the wildness of Mamo and the tranquility of Cagliostro. Even though it builds to larger-scale action, its TV budget means that the scale and writing aren't as expansive and impressive as the theatrical entries – and therefore more representative of what to expect from most of the series!
All in all a very solid introduction to both series and cast.