Audiences love this play and they should. There is a lot to like and enjoy. I think upon repeated readings Henry becomes a more equivocal character than he seems at first. And readers of the King Henry IV plays will know him before he became King Henry and know something deeper about his personality.
And of course there is the whole bit about the drive to France being sponsored by the Church to avoid confiscation of property by the Crown. Moreover, there is the slaughtering of the French prisoners, and his treatment of Falstaff (who dies offstage in this play). This isn't revisionist stuff, it is right there in the play, but it is easy to miss the first time you are trying to take in the play.
In any case, this Arden edition is the one to buy and read from. Why? Because it has the most authoritative text, but that is only the beginning. It also shows variants between the early sources. The notes at the bottom of each page of the play are simply fabulous. The editor includes not only helpful notes explaining what might be obscure in the text of the play, he provides sources Shakespeare probably used such as Holinshed and makes for some very interesting study. There are also some helpful notes on how various scenes have been performed over time.
And to make this sound more like an infomercial, you get more! The introduction provides great background material on the play, its sources, and how it has been performed throughout history. After the play, there is a photo reproduction of the first Quarto from 1600 and it is fairly readable. There are also a couple of maps showing the path of the English Army from Harfleur through other towns on its way to Calais and makes clear how they had to pass through Agincourt.
There is also a helpful genealogical table so you can see the confusing claims used by Henry and the French nobility to make their claims. And there is a doubling chart so you can see how theater companies can perform all the roles with fewer actors.
This is a great edition as are all the plays published by the Arden Shakespeare. The amount of work collected in these volumes is stunning and they will enrich your experience of the plays tremendously. I can't recommend them enough.