If you were interested in getting into the Marx Brothers, I recommend beginning with A Night At The Opera.
Why Opera and not Duck Soup, or Animal Crackers, or A Day At the Races? Or [insert any Marx Brothers film here]?
A Night At The Opera was their first film with MGM after the contract with Paramount ended. What most fans enjoy about the Paramount films is the anarchic chaos and when the brothers went over to MGM, Zeppo left (he was usually the straight man), leaving Groucho, Chico, and Harpo. Gummo never appeared in the films and never really developed an onstage persona like the rest of his brothers. It's my opinion that A Night At The Opera serves as a great way to bridge the gap between the anarchic Paramount films and the slightly less anarchic MGM films.
MGM wanted more of a plot and a story where the brothers were clearly against a villain, or at least an antagonist. In their earlier films, they were more ambiguously good and unpredictable. A Night At The Opera maintains much of their anarchic behavior, but also casts them as good guys trying to right some wrong. Opera has the brothers fighting high society and attempting to bring two young lovers together, which then brings chaos to an ocean liner as well as a production of the opera Il Trovatore in New York City.
A warning though: if you're actually going to watch the Marx Brothers--pay attention! You have to watch and listen to these films. The word play and the gags are almost non-stop and the results aren't always immediately apparent. If you look at the Three Stooges, they can be funny, but are more of a one-trick pony in that they rely mainly on slapstick (basically finding new ways to hurt each other), but the Marx Brothers have it all--slapstick, witty wordplay, and clever situations that allow for great gags (a packed stateroom aboard an ocean liner or a two bedroom apartment where they switch all the furniture right under the nose of a cop making him believe he's going mad).
Groucho's characters usually direct the chaos, but with sharp wit and occasionally breaking the 4th wall. He begins most of the films having a position of some sort or a person of standing, even if it's been entirely fabricated or it's a sham.
Chico's (pronounced Chick-O) characters are often a partner or friend of Harpo's characters. Chico usually has a scheme of some sort. Most of the films have a sequence where he plays the piano--he's very entertaining to watch play, as his fingers dance upon the keys in unusual ways--he'll make you laugh just watching him play. Chico and Groucho often have a long exchange (over a contract for instance), but from what I've read, they ad-libbed quite a bit during the routines one-upping each other.
Harpo's characters never speak (well, there was one time where he sang from inside a barrel, but it was brief), and he's the most unpredictable and chaotic of the three. His coat is packed with an odd array of items and he's often relieving people of their possessions and toying with them. Like Chico with the piano, Harpo is usually given a sequence where he plays the harp. His playing is magical and engaging--he doesn't play the harp in a way to make you laugh like Chico with the piano, but it's enjoyable and easy on the ears.
Start with A Night At The Opera, and if you enjoy that one, try A Day At The Races. If you're still curious and want more, I'd say go with Duck Soup. At this point, you've been warmed up to the Marx Brothers and will enjoy Duck Soup--it's also the final Paramount film and last film in which Zeppo appeared. Many fans of the brothers cite Duck Soup as their favorite (it's my second favorite, after Opera, of course).
What makes the Marx Brothers so special is the variety and range they display--they could do it all. Music, singing, dancing, wordplay, physical comedy were all a result of their stage careers as vaudeville performers. I can't think of anyone today who could pull off what the Marx Brothers did so effortlessly, and at a time when talkies were new and special effects didn't drive films. Modern comedies simply cannot stand up to the Marx Brothers at their best (maybe even at their worst).
There are a few collections out there, a Paramount set as well as an MGM set. Turner Classic Movies sells them as does Amazon and Barnes & Noble. You may even be able to stream them (since I own all the films I haven't investigated that option).