Nearly all of Black Panther's comic book history is free on @comiXology. Here are my recommendations for getting into the character:
1/

Rise of the Black Panther is a retelling of T'Challa's origin story, and what i consider the definitive version of it. If you've never read Black Panther before, start here.

https://www.comixology.com/Rise-of-the-Black-Panther-2018/comics-series/109611

2/

Christopher Priest totally redefined the Black Panther as a character, adding political intrigue and sophistication to the franchise. This is the run that took Black Panther into the modern age.

https://www.comixology.com/Black-Panther-1998-2003/comics-series/9901

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Ta-Nehisi Coates is the current writer of Black Panther, and a damn good one at that. While earlier writers had moved away from the political nature of the character, Coates brings it back in full force.

https://www.comixology.com/Black-Panther-2016-2018/comics-series/69142
https://www.comixology.com/Black-Panther-2018/comics-series/115301

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Marvel Action Black Panther is my number one choice for younger readers wanting to get into Black Panther. It's not just limited to kids, however, it's got a great story for all ages.

https://www.comixology.com/Marvel-Action-Black-Panther-2019/comics-series/136128

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Jack Kirby co-created Black Panther with Stan Lee, and later returned to write the character solo. This is a frankly bizarre book, unlike anything else on the list, but still has some interesting ideas and great art.

https://www.comixology.com/Black-Panther-1977-1979/comics-series/64172

6/

Killmonger is not about the Black Panther; instead, it is about his greatest adversary before he became the man who would toss T'Challa off of a waterfall.

https://www.comixology.com/Killmonger-2018-2019/comics-series/124018

7/

Honorable mentions go to Don McGregor's work, as it is some of the most important work done in black panther's history. Unfortunately, it's not free. Nonetheless, here are the links if you're interested:

https://www.comixology.com/Black-Panther-Epic-Collection-Panthers-Rage/digital-comic/428436
https://www.comixology.com/Black-Panther-Panthers-Quest/digital-comic/580356

I think that's all I have for now. If I think of any more, I'll add to this thread below.

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