I would suggest The Grand Budapest Hotel without a doubt.

As someone who's watched all Wes Anderson films as they were released and gone back over the years to rewatch them, my opinion is that Rushmore and The Royal Tenenbaums are his best 2 films. I think out of those two Royal Tenenbaums is the fan favorite, but the more I watch Rushmore, the more I'm starting to think it's the better of the two overall. Jason Schwartzman, the lead actor, was 16 when it was filmed and he absolutely owns the role.

A lot of people, including myself, are starting to think Anderson is going a little overboard on the "quirkiness" factor in his newer films. I still think they're good. I just think the focus on the quirkiness is detracting from character development and soundtrack and story overall.

Grand Budapest is one of the "newer" ones that captured the vibe of the older movies. Still don't like it as much as Rushmore or Tenenbaums, but it was up there. The Life Aquatic is somewhere in between the new and old eras. I've always enjoyed it. The talented cast kind of helped save the story a bit on that one.

Generally speaking, I'd say go from old to new. You can maybe skip Bottle Rocket (his first) until later as it's kind of its own experimental first movie before he found his niche.

Anderson is a love him or hate him director. I've always found his films unique and fun. A breath of fresh air.

I would highly recommend Rushmore. Darjeeling limited, the royal Tenenbaums and grand Budapest hotel. These films would bring a smile to your face and they have a lot warmth. Unfortunately I’ve found a lot of his recent films very self indulgent and definitely don’t watch asteroid city to start off. This may sound controversial to his fans but I strongly feel he has become a self parody now

The Life Aquatic is my favorite :3

Just know that if you don't like one, chances are pretty good none of them are for you.

Just for science I would be fascinated to see what your opinion would be if you started with The Phoenician Scheme that just came out.

It's such pure, unadulterated Wes Anderson tropes that I wonder what a newcomer with your level of interest would take to it. Would it be fun or impenetrable?

That said: Royal Tenenbaums would be a strong safe start otherwise.

Rushmore. Early Anderson is somewhat less mannered and does outbreaks of anarchy way better thanks to Owen Wilson’s co-writing. It’s obviously semi-autobiographical and Fisher’s elaborate stagings of 70s movie classics are amazing.

Isle of Dogs yo

I don't think I had seen a Wes Anderson movie until about 3 years ago when I watched one with friends.

It was 'The Life Aquatic with Steve Zissou', and my reaction to it prompted a friend of a friend to suggest that maybe I should watch more of his movies.

Now, I am no fan of certain directors or produces and know/recognise their work. I just like a movie because I like the movie.

So I cannot say if this is a good one to start off with or how good it is compared to other works of his.

Edit:

Wait, I lie.

I watched The Grand Budapest Hotel a few years before The Life Aquatic and I enjoyed that one as well.

I didn't realise that was one of his as well, but I had a hunch and looked it up.

Royal Tenenbaums would be my recommendation. It's fairly close to the start of his ouevre but his style had been given a chance to develop a little bit by that point.

Fantastic Mr Fox is one of my favorites. His visual style is reminiscent of children’s illustration books, so why not start with an adaptation of a children’s book?

The two best Wes Anderson movies, according to me:

Life Aquatic with Steve Zissou

Asteroid City

Life Aquatic is just all around good. Probably don't need any kind of esoteric knowledge to understand any of the humor or plot. Asteroid City, on the other hand, might hit harder if you are or ever were a theatre kid.

Honestly, just skip his work altogether.