Start with On Basilisk Station. It is the first book, the series is strictly sequential, and it happens also to be the best possible entry regardless of that: one ship, one neglected star system, one officer given a bad posting and an impossible problem. It is short by the standards of what follows, and the final engagement is the sequence that has sold the series for thirty years.
Read the main line in publication order, which is also chronological order: On Basilisk Station, The Honor of the Queen, The Short Victorious War, Field of Dishonor, Flag in Exile, Honor Among Enemies, In Enemy Hands, Echoes of Honor, Ashes of Victory, War of Honor, At All Costs, Mission of Honor, A rising Thunder, Uncompromising Honor. There is no publication-versus-chronological controversy in the main sequence. The complication is elsewhere.
What you are actually reading
This is the Napoleonic naval novel moved into space, and Weber has never pretended otherwise. Manticore is Britain, the People's Republic of Haven is revolutionary France down to its Committee of Public Safety and its political commissioners attached to naval officers, and Honor Harrington's initials are not a coincidence. If you have read Forester or O'Brian, you will recognise the shape of almost every plot before it arrives, and for most readers that is the appeal rather than a complaint.
The honest warnings
The technical exposition is real and it is heavy. Weber built a consistent physics for his sublight drives and missile engagements and he explains it, at length, repeatedly, including in the middle of battles. Some readers love this. Others skim it, and skimming costs nothing.
The scope inflation is the bigger problem. The first six books are naval adventure novels with Honor at the centre. From Echoes of Honor onward the cast expands enormously and the books become political and strategic novels with dozens of viewpoint characters, many of whom you will not remember. War of Honor is where this is most pronounced, and it is the book most often named as the low point for pacing — a great deal of diplomacy and very little of the thing you came for. It is also load-bearing for everything after it.
The tone shifts too. Field of Dishonor is where the series stops being an adventure: a personal vendetta, a duel, and a coldness that the earlier books had not shown. In Enemy Hands is the darkest of the run, involving Honor's capture, permanent injury and an execution set-piece. There is torture, there are mass-casualty engagements described in numbers, and the middle of the series is considerably grimmer than its first three books suggest.
The spin-off problem, and what to do about it
This is the genuine reading-order question. The main fourteen are not the whole story: there are several spin-off subseries following other characters and other theatres, plus anthologies, and events in them are assumed by the later main-line books. Weber and his publisher have circulated an interleaved order that folds everything together chronologically.
The recommendation here is to read the main fourteen straight through first. The interleaved order asks a new reader to keep track of four sets of characters before they have finished caring about one, and the main line remains readable without it — you will occasionally register that something happened offstage between At All Costs and Mission of Honor, and that is the cost. If you finish the fourteen and want the offstage material, go back and read the spin-offs then, when you have reason to care who those people are.
Where to stop
Ashes of Victory is the real stopping point and the one to plan for. It closes the first war arc, it resolves the personal threads the first nine books built, and a reader who ends there has a complete story with a proper ending. Everything after it opens a second and much larger conflict.
If you want that conflict resolved, Uncompromising Honor does resolve it, and the four books between are the price. Do not start the back half casually. More military science fiction reading orders are on Discover.
Follow the full ordered path here: Honor Harrington Reading Order: Where to Start with David Weber.