Are the 3 main genres within classical music Baroque, Romantic, Classical?

Classical music is an overall genre: another term for it is (western culture) art music.

There are numbers of historic periods, named in the late 1800's when music history was for the first time, being formulated. The period names are attached to he music from them, and mark a general style difference in each, as developed over time.

Medieval

Renaissance

Baroque

Classical

Romantic

Modern

Contemporary

[Different sources split up the 20th century differently, or into smaller sub-groups. The (Oxford) Groves Dictionary -- used in music schools throughout the English speaking areas of the world, keeps it more 'wide' and has Modern 1890 - 1975; Contemporary from 1975 onward.]

For the general public, or the 'average' classical listener, most of what is listened to and performed come from the Baroque, Classical and Romantic eras -- i.e. those are the most common taste. More 'devoted' classical fans often know some, at least, of music from all the different periods.

You can find a list of composers representative of each period in the big Wikipedia article, "Classical Music," not far down under the sub-heading "History."

http://en.wikipedia.org/wiki/Classical_music

a click on the links in the box on the right -- medieval classical,' etc. leads you to those lists of composers from those periods.

Genre: within classical music has to do with pieces typed by numbers of instrumental forces, and vocal music.

Solo instrumental music:

Music for one instrument solo. I suppose the biggest body of literature and the best known would be keyboard music, organ, harpsichord, piano.

Chamber music:

music for only several players, say two to about ten - usually played without a conductor. Duet, Trio, Quartet, Quintet, Sextet, Septet, Octet, Nonette, denote the number of instruments needed for those pieces.

Orchestral music:

Music for larger ensembles, a 'chamber orchestra' being about 30 to fifty players, a full orchestra "symphony orchestra" fifty up to the larger ensemble of about 100, sometimes even more, players.

Vocal music:

for voice, often with an instrumental accompaniment.

Choral music:

is music for choirs alone, also "Acappella" means unaccompanied voices.

Choral piece: the genre of works for orchestra and chorus, sometimes also vocal soloists.

Best regards.

P.s. as per 'niche' style, I suppose there are one or two, usually either an eccentric composer who just does not fit in, by style, with all going on around them. By date, Eric Satie was a 'romantic' composer, but his music is anything but. It has been called 'modern,' and 'Dadaist' while it sits somewhere apart on its own.

Ditto for, especially, 'Impressionism.' That is a style, not so much an historic era, and its two main proponents, with a few far lesser composers lumped in under the style, were Debussy and Ravel.

Some notable composers in each style are as follows:

Renaissance: Purcell, Palestrina

Baroque: Vivaldi, Bach, Telemann, Handel.

Classical: Mozart, Beethoven, Haydn

Romantic: Berlioz, Tchaikovsky, Rimsky Korsakov

Modernism: John Cage, Toru Takemitsu, Gyorgy Ligeti

Neoclassicism: Eric Satie, Stravinsky, Francis Poulenc

The Late Romantic/ Modernist transmission period: Mahler, Shostakovich

Atonal: Arthur Schoenberg, Alban Berg

Minimalist: Phillip Glass, John Adams, Michael Nyman

The Wagner School: Mahler, Richard Straus, Lizst, Humperdink

Don't forget Ars Antiqua, Ars Subtilior, Ars Nova and Rococco

Yes, but not in that order.

All of this seems very homework like.

... Hoping that petr b's answer is more than adequate to get you that A you so richly deserve for your research.