Michael Crichton kind of set the standard with his novel Sphere, in which those called in are: psychologist, mathematician, zoologist, astrophysicist and marine biologist. The marine biologist had to do with the plot, so we could look to The Arrival, where a linguist is a core part of the team. Jack McDevitt took a slightly different approach with The Hercules Text, which included a priest, a psychologist, a "scientist," a national security person, and a few bureaucrats. The religious angle I think is interesting, though I personally wouldn't choose a religious person for the contact.

For me, I think we need a behavioral psychologist (to study aliens without words), an astrophysicist (to learn about their system and how they got here), a math genius specializing in quantum mechanics (to share what we know about the fundamental parts of the universe), a linguist (however they communicate, we can try to decode it), and a biologist (to study their biological forms and explain our own).

Mathematician for communicating because math is math everywhere

Linguistics for expert in communication

Philosopher because nonstandard nonlinear thinking

Astrophysicist because the aliens are from somewhere else

Chuck Norris

4 cultural anthropologists with specialized skills in decoding/translating languages as well as ethnology skills to record important cultural customs. And probably one painter or musician to show that we are creative, introspective, and peaceful. Honestly if they made it to our solar system they are not going to care about our interpretation of physics, math, chem, or biology, they would have that covered.

You ever see the movie/ read the book "Sphere"? Basically that.

A Mathematician, as that will probably be the closest to a universal language.

An Astrophysicist to locate similar stars.

A Biologist (as well versed as possible in several disciplines) to try to understand their biological makeup.

A High ranking military official to secure any resources necessary to smooth over first contact.

And a Psychologist to help the team cope with the absolute madness/terror of witnessing something no living organism on this planet has ever experienced. Preferably a Behavorist to try and understand the behavioral patterns of the aliens.

A philologist to decipher the language, an astrophysicist to pinpoint where they came from, an epidemiologist to prevent the spread of unknown diseases, a cinematographer to display Earth culture through media to help the aliens understand us, and a stand-up comedian because it would be funny.

Ethologist for sure, not just a "biologist", or a psychologist whose head is stuck exclusively up human ass.

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Anthropology, linguistics, sci-fi author/expert, artist, biologist.

As ‘broad-spectrum’ as possible; intelligence AND specialty. Except the sci-fi person - space, alien, contact oriented as compared to human only sci-fi

Bonus point: child