Well his work breaks down into this:
Three romantic Operas: --- none of these are his masterpieces, they stick (at least more than his later works) to German operatic conventions of the time, and are overshadowed by his later works, but they are still very good in their own right.
Der fliegende Holländer
Tannhäuser (Not to be missed, get the Gwyneth Jones' Bayreuth version of 1978 on DVD, pirate it or something, remember to find good quality torrents)
Lohengrin
Wagner then abandoned 'Opera' (to return in Meistersingers), in favour of different genres of 'music drama' he created, all his late works here are considered his masterpieces:
Bühnenfestspiel:
(aka. the Ring cycle)
Das Rheingold
Die Walküre
Siegfried
Götterdämmerung
This is his magnum opus and it'd be good to start with it. Levine's Metropolitan opera version is grotesque in that they spent too much money on massive constumes trying to make it a traditional version, and the singing is flat, music is good however, but the acting is atrocious and nobody moves on the stage. The Barenboim/Kupfer version now on blu-ray is one of the best recent productions, with brilliant singers and actors, superb music, but the costumes are just a little dated in that it'd take a little getting used to. It doesn't patronize your imagination though and isn't as ridiculously over-dressed as Levine's version, very well made --- I consider it the best production.
Then there's the French version of Boulez and Chereau, the Jahrhundertring (Centenary Ring). This is another brilliant production, with the setting controversially modernised, but introduced movements and stagings which are now considered classic and iconic.
Someone new to the Ring should watch the Barenboim Kupfer version, it's excellent and doesn't actually (despite it's modernized design) in fact change any of the fundamentals of the Ring, the Rhinemaidens are not cancan dancers as in Chereau's version, the Gods are not aristocrats for instance, the subtitles which come with the blu-ray are perfect too.
Barenboim/Kupfer's version is full of movement and the characterisation superb, before watching however you want to read up a little on the basic outlines of the Ring cycle, there are good companion books (for all the operas) such as pic related, which has the entire libretto (and is great to read because the Ring is a poem on it's own account), but you don't need to be a scholar, you can dive in.
Handlung: (Literally 'Act', as in a single dramatic and musical movement)
Tristan und Isolde
A masterpiece, Barenboim and Chereau's 2015 edition is a good one. It's also a good starting point, though by no means does that mean it's for beginners. It's up there with the Ring. Incidentally Nietzsche's favourite.
His only late Opera, comedy:
Die Meistersinger von Nürnberg
Bühnenweihfestspiel (consecreated stage festival play):
Parsifal (last work, to be approach last).