I'm not familiar with the Hackett publishing (is it this one?), but Keatinge and Maudslay are very well known English translations.

Keatinge was, I believe, the first English translation, published in 1800. The problem with this version, and all English translations before Maudslay, was that it was working from a 1632 Spanish publication, which contained additions and deletions by a Spanish friar, as well as by Díaz del Castillo's son. The additions tend to emphasize the inevitability of Spanish triumph and spend more time on portents, omens, etc., while the deletions are typically in the vein of removing more embarrassing and egregious Spanish behavior.

It was not until 1904 that a Mexican bibliophile, historian, lawyer, Genaro García, obtained a copy of one of DdC's original manuscripts from Guatemala, where DdC lived out his later years. García then published this copy, which did not include the later edits. Maudslay's English translation of this was subsequently published in 1908 by the Hakluyt Society, and is considered the authoritative and seminal version.

Keep in mind though, that Conquest, in it's original form, is not a quick account. It is something like 1000 pages and is often repetitious, digressive, and with chapter organizations which can seem baffling to a modern reader. As such, most publications are abridgments, or at the very least attempt some effort of cleaning up the organization of the text. You should check to see if any version you'll be picking up ends with the surrender of Cuauhtemoc and a triumphant Spanish victory. The original Guatemalan manuscript continues on considerably after that point, where the Spanish veneer of bringing Christendom slipped off in a scramble to establish themselves as hidalgos nuevos.

Older texts also tend to omit any clarificatory footnotes, contextualizing introductions, or other guideposts for less familiar readers. Most modern abridgments try to place the narrative within the history of DdC's own limited viewpoint, his fued with Gomara, and the larger historical events. I find my increasingly battered copy of Davíd Carrasco's 2008 abridgment, based on the Guatemala manuscript and Maudslay's complete work, to be excellent in this regard. A quick glance at the Hackett publication appears to an excellent job at this well, as is properly based on the Guatemala manuscript, and I'm probably going to add it to my collection.

So, start with the Hackett text, then go back after (or during) and do some comparative reading with Maudslay. If your library has an unabridged version of Maudslay, do take some time to look over where the Hackett text made abridgements. Sometimes this can be interesting, though more often it is a completely understandable attempt skip over BdC repeating himself.

One final reading note, and this is just my own personal approach to the text, is to remember that DdC didn't start writing his book until some 30 years after the Spanish Invasion. Part of what prompted him to do this is money, but also part of what prompted him was the publication of a hagiographic biography of Cortés by his secretary, Gomara, in the early 1550s. (Comparisons with that work are fun as well, since DdC has some parts where he was clearly "influenced" by Gomara in his own writing.) Good Ole Bernie would work on his manuscript up until his death, decades later, never seeing it published. I like to think a large part of what prompted him to keep writing was not so much money or spite, but also a curmegeonly insistence on telling his side of the story.

While the events in the text occur when DdC was a young and vigorous man, I sometimes find the text more relatable if you think of the narrator not as young conquistador Bernal, but old and crotchety Bernal. He's the increasingly doddering uncle who wants to tell you how it really happened in The War, because you kids today are fed a bunch of nonsense and you don't understand.