Start with Asterix and Cleopatra. The obvious move is Asterix the Gaul, the 1961 first album, and it is the wrong one: the drawing is stiffer, Obelix is barely a supporting character, and the travel-and-satire structure that defines the series has not been invented yet. It is a curiosity best read tenth, when you can see how much was still to come.
Asterix and Cleopatra is the sixth album and the first that is unmistakably the mature series — a full-scale parody of the 1963 Hollywood epic, a palace-building wager with Caesar, and Albert Uderzo drawing crowds, architecture and slapstick at the top of his ability. Nothing in it depends on anything you have not read. That is the important structural fact about Asterix: the albums are self-contained. There is no plot to follow across them, only a village that resets at the end of every book with a banquet and a bound-and-gagged bard.
The albums most readers rate highest
After Cleopatra, read Asterix the Legionary, which puts Asterix and Obelix through Roman army conscription and is the tightest joke-per-page album in the series. Then Asterix and the Roman Agent, in which Rome sends a single man whose only weapon is the ability to sow suspicion, and the village tears itself apart; it is the one most often named the funniest.
Mansions of the Gods is the satire of urban development — Caesar decides to civilise the Gauls by building a housing estate next door — and Obelix and Co. is the satire of market economics, with a young Roman efficiency expert persuading Obelix to industrialise menhir production. Those two are the sharpest things Rene Goscinny wrote, and they are funnier if you have already met the village at rest.
The travel albums
Asterix in Spain, Asterix in Switzerland, Asterix in Corsica and Asterix in Belgium run the same engine: the pair leave the village and the album becomes an affectionate catalogue of national stereotypes. Asterix in Corsica is widely held to be the best-loved of the series in France and the one that travels worst, because a large share of the jokes are local. Asterix in Belgium was in production when Goscinny died in 1977; Uderzo completed it alone.
Asterix at the Olympic Games, Asterix and the Laurel Wreath and Asterix and the Chieftain's Shield belong to the same middle stretch and are all solidly good without being anyone's favourite.
What our list does not have, and why that matters
Our catalogue holds thirteen of the twenty-four albums Goscinny co-wrote, plus Asterix and the Great Divide, the first that Uderzo wrote as well as drew. This is not a complete run and should not be treated as one. Four of the albums most often placed among the best are absent from it: Asterix in Britain, Asterix and the Big Fight, Asterix and the Soothsayer and Asterix and the Golden Sickle. If you finish the list and want more, those are the next four to find.
The post-Goscinny albums are a genuine drop and most readers say so. Asterix and the Great Divide is competent and thin — the writing is where you feel the loss, not the art. Since 2013 the series has continued under Jean-Yves Ferri and Didier Conrad, which is a separate question again.
The translation is part of the achievement
The English Asterix is the work of Anthea Bell and Derek Hockridge, and it is not a straight translation. The French names are puns and so are the English ones, invented rather than carried across: Getafix, Vitalstatistix, Cacofonix, Dogmatix. Any edition you buy in English will use their names, so the choice is not really open to you, but it is worth knowing that the wordplay you are laughing at is largely theirs.
Where to stop
Read the Goscinny albums and stop. That is the honest answer, and it is the one most long-term readers give. If you want a short course rather than the full run, five albums will do it: Asterix and Cleopatra, Asterix the Legionary, Asterix and the Roman Agent, Mansions of the Gods and Obelix and Co. Browse more illustrated reading on Discover.
Follow the full ordered path here: Asterix Reading Order: Where to Start and Which Albums Are the Great Ones.