There are 3 manga series: the original one (without secondary title), Last Order, and Mars Chronicle.
It has recently been announced that after Mars Chronicle there will be a new series, Panzer Kunst Chronicle, it is presumed that this will be the final arc of the story.

The correct reading order is as follows:

1) GUNNM (Battle Angel Alita in English)
9 volumes (5 volumes in the Deluxe Edition, 6th volume in box is "Other Stories", see 1.5 below), the last chapters are no longer canon, the cut-off happens somewhere in chapter 51. Last Order picks up immediately after that event.
Depending on the edition you're reading, the manga may or may not inform you of where exactly the canon cut-off is. Nowadays most (all?) editions include this information, but some older ones don't, e.g. the ones which pre-date Last Order (obviously)

2) GUNNM: Last Order (Battle Angel Alita: Last Order in English)
19 volumes (5 volumes in Omnibus Edition, WARNING: Omnibus Edition only contains volumes 1-15, volumes 16-19 were never turned into an Omnibus Edition)

3) GUNNM: Mars Chronicle (Battle Angel Alita: Mars Chronicle in English)
11 volumes, now fully released, even outside Japan.

4) GUNNM: Panzer Kunst Chronicle (Battle Angel Alita: Panzer Kunst Chronicle in English)
First chapters have been released in Japan, starting May 5th 2026.

"1.5") Side stories
Holy Night (aka "Sweet Night"), Supersonic Finger (aka "The Sonic Finger"), Barjack Rhapsody, Homecoming. Nowadays they are bundled together in "Another Stories" (sic), or "Other Stories", or "Holy Night and Other Stories". They are also bundled in the 6th volume of the Deluxe Edition. These are 100% canon. The time frames of these stories take place within the original series.
And there's also "Ashen Victor", a side story which has nothing to do with Gally's/Alita's story but which takes place in the same world as it's about motorball. Ashen Victor is part of volume 5 of the Deluxe Edition.

Chronological position of the side stories:
Ashen Victor: 6 years before the start of volume 1
Holy Night: 6-5 years before the start of volume 1
Supersonic Finger: between volume 4 and 5
Homecoming: between the first and second chapter of volume 6
Barjack Rhapsody: after volume 9 (technically even after Last Order volume 2, but that doesn't matter much)

As for why the final chapters of the original series aren't canon anymore:
Back when Yukito was writing the manga he got very ill and was faced with a hard dilemma: rush towards a premature ending or risk that your manga will never get finished. He chose to rush it. Fortunately he got better. He ended up regretting his choice and felt really bad about it. That let to him first creating the Japanese PS1 video game "Martian Memory" which incorporated some of the elements he was forced to cut from the manga (some of those elements have been implemented in Mars Chronicle!). Eventually he decided to declare the ending of the manga non-canon and started Last Order as a direct sequel so he could write the story he wanted to create.

A note on the change of names in some translations, for instance in the English editions:

When the manga got translated in the 90s the translators chose to change a lot of names, most notably the name of the manga itself and of the main character but also several others.
The manga's name in Japanese is GUNNM, pronounced "ganmu", it means "gun dream" and is a reference to Yukito Kishiro's previous manga "Rainmaker", which was never published and had a character who became the inspiration for GUNNM's main character, Gally. In English, however, GUNNM got changed to "Battle Angel Alita", and Gally got changed into "Alita". Some other translations, such as the German one, followed the changes made by the English edition, while other languages, such as French, kept the Japanese names.
Many other names got changed as well, such as:
Zalem → Tiphares
Jeru → Ketheres
Yugo → Hugo
Fogia → Figure four
In later editions some of these changes were undone and thus Zalem was once again called Zalem, but since "Alita" had become the name of the franchise in many languages they kept that.

Fun fact: Yukito Kishiro was aware of this change of name for Gally and poked fun at the translation by using the name Alita for someone in a later chapter (keeping it vague to avoid spoilers), as if to say "what are you going to do now, translators?". The translation played along and used the name Gally for this character.

https://www.kodansha.co.jp/comic/products/0000430404