Vtyjkyuk

My guess is that it is:

Lin Manuel Miranda

Because:

The ellipsis after "Absolutely!" is three periods, or 'stops'; Lin in dialectical Scots English, cognate with Danish, Swedish and Icelandic, means 'to pause, rest, or stop'.

And:

"Man" and "Well" are given as first words in sentences = Manuel

And:

Bizet's most famous work is Carmen, and a famous Latin American performer is Carmen Miranda.

And:

You had it true = you had it right. At the beginning, we have three stops, a stop in music denotes silence. To Mirandize someone is to read them their rights: you have the right to remain silent, hence Miranda again.

This is an interesting puzzle, and I'm not sure what to make of anything...

The four composers that Pete mentioned were all Romantic-era composers; so maybe Pete really likes Romantic-era composers? In which case he could appreciate the "founder" of the Romantic era, Ludwig van Beethoven, whose bold works near the end of his career (See: Choral Symphony) ushered out the Classical era of his youth and brought in a new Romantic era. (It's also quite possible he appreciates Frédéric Chopin, since he was representative of that era as well and has connections to Paris along with many of the composers mentioned.)

Second Guess

Could it be

Piotr Il'ich Tchaikovsky? A Romantic-era composer from around the same time as the four mentioned, whose name is also Pete?

Third Guess

Could it be

(Saint) Hildegard von Bingen, a 12th century nun and one of the most famous composers of plainchant of all time? This might be because the concert band's name was Plain Inspiration, referencing the fact that Pete might have been inspired by plainchant.

Feedback: Overall a pretty good riddle -- I think that it may need to have a few more tags added (say, knowledge) because the answer is not inherently obvious without that extra knowledge. (I certainly don't even think my answer is correct.) The grammar could be cleaned up a bit, because it affects the readability of the puzzle. I hope that there's a more slam-dunk answer than mine, although am I on the right track?

Would his favorite composer be:

Gustav Holst?

This is based on the phrase "said the true from the beginning" in combination with "an answer in the future".

In which he came first in your list, but was born in 1874 and was the last born on your list.

Second Guess

Georges Bizet

Whom is also my favorite (due to Carmen) aside from Beethoven (I know cliché, but who can resist Moonlight Sonata).

My second guess is also based on "said the true from the beginning". In which:

Georges Bizet was born in 1838 and came first out of all the named composers.

Third Guess

Based on what El-Guest has supplied, I believe it would be:

Inspiration Orchestra

On the basis that:

You have stated no research is required and that the answer is contained in the riddle. Also, I had originally thought of this, but I believe I was over-thinking it and I was looking into Plain Inspiration on Google.

My Thoughts

As a whole, your post is well formatted; it could use a couple grammar changes (in my personal opinion, but to each their own; I'm not one to nitpick on this). The back and forth between Pete and Dave is quite a nice style riddle (conversations with hidden answers are often fun to solve), and the answers seem to be located somewhere in your riddle.

Also building on what El-Guest has stated below, I would definitely recommend additional tags for this. Knowledge definitely fits, Wordplay is a possibility. Feel free to research the available tags and determine which best fit your puzzle!

This was a great first post! Welcome to Puzzling.SE!

Is it

The Dependency Manager for PHP Composer?

Because

Composer has a poorly designed logo - it is a conductor, not a composer, and it has nothing to do with the previously mentioned composers or music at all. I couldn't make sense of this based off of the actual riddle, though.

EDIT:

Okay, also Pete says "Okay, this almost seems like you said the true from the beginning. Maybe you will find an answer in the future." So instead of saying "truth", he says "true", which is a boolean value used in PHP.

Pete's favorite composer is

Dave. Pete already said that every musician who likes classics has a favorite composer. Dave likes classics, but does not have a favorite composer. Therefore, Dave is not a musician. However, Dave had a role in the band but NOT as a musician. He was the composer, therefore Pete's favorite composer was Dave himself.

Guessing, because I realized something but don't want to actually make the profile. I don't know if bands count, but I realized something. Hint 3 says that "Every line of the conversation is important." The ]right answer was "almost... at the beginning." The second line of the dialogue is "..."- an ellipsis. A quick look at Wikipedia's disambiguation page shows two albums by that name. One is by Scorn, which is electronic music, so I realized, as I'm typing this, that it probably isn't that. The other album is by a Scottish alternative rock band called Biffy Clyro. https://en.wikipedia.org/wiki/Ellipsis_(Biffy_Clyro_album)#Track_listing In the "Track Listing" section, it says that Simon Neil wrote all the songs unless they note otherwise, and he's still involved when those notes exits. He is credited as a songwriter, which I feel implies lyrics whereas "composer" implies writing the music. However, the article also says he wrote the songs and lyrics, thus qualifying him as a composer as well. Therefore, I believe Pete's favorite composer to be Simon Neil from the band Biffy Clyro.

This is a complete guess, and I doubt it's the answer; but:

Is Pete's favorite composer David Petersen?

This guess is based on:

The two names used are Pete and Dave which are typically short for David and Peter.

Well, this took a bit of research and still is kinda vague. But, oh well...

Answer

All-4-One.

The song "Here is my heart" has the following in the lyrics: "With every revolution shows the answer is in the evolution. Turning...spinning...moving on". This fits into what Pete says about the answer being in the future.

"Every musician who likes classics has a favourite composer", we could say All. 4 Composers are named. Pete asks for only One. All-4-One.