Pre-Baroque and early Baroque:
1. Very important: William Byrd, Orlando Gibbons, Henry Purcell, Lully, Frescobaldi
2. Not so important: The Fitzwilliam Virginal book, John Bull, Giles Farnaby
3. Obscure: John Munday, Martin Peerson, Peter Phillips, Thomas Tomkins
Baroque:
1. Very important: J.S. Bach, Scarlatti, Handel, Telemann, Rameau, Couperin
2. Not so important: Thomas Arne, John Blow, Jeremiah Clarke, D’Anglebert, Dandrieu, Dacquin, Jean Baptiste Loeillet, Domenico Alberti, Domenico Cimarosa, Benedetto Marcello, Pietro Paradies, Pasquini, Pergolesi, Pescetti, Ferdinando Turrini, Domenico Zipoli, Mateo Albeniz, Antonio Soler, Carlos Seixas, Dietrich Buxtehude, Froberger, Kuhnau, Krebs, Kirnberger, Gottlieb Muffat, Pachelbel, Sweelinck
3. Obscure: William Croft, Chambonieres, Jacques Duphly, Elizabeth de la Guerre, Azzolino della Ciaja, Giovanni Grazioli, Gianbatista Martini, Giovanni Picchi, Giovanni Platti, Michelangelo Rossi, Giovanni Rutini, Rafael Anglos, Cantallos, Narciso Casanovas, Mateo Ferrer, Freixanet, Jose Galles, Felipe Rodriguez, Blas Serrano, Sousa Carvalho, Rodriguez Coelho, Frei Jacinto, Johann Eberlin Johann Fischer, Carl Heinrich Graun, Samuel Scheidt, Georg Wagenseil
Classical:
1. Very important: Mozart, Haydn, Beethoven
2. Not so important: C.P.E. Bach, J. C. Bach, W. F. Bach, Clementi, Dussek, Hummel
3. Obscure: Hassler, Mehul
Romantic:
1. Very important: Chopin, Liszt, Schumann, Isaac Albeniz, Brahms, Grieg, Faure, Granados, Mendelssohn, Schubert, Tchaikovsky
2. Not so important: Alkan, Arensky, Balakireff, Borodin, Chabrier, Dvorak, Cesar Franck, John Field, Niels Gade, Glazounov, Godowsky, Gottschalk, Mussorgski, Respighi, Saint Saens, Smetana, Sgambatti, Weber
3. Obscure: Sterndale-Bennett, Ferucio Busoni, Chaminade, Gliere, Amy Beach, Gurlitt, Heller, Kirchner, Fuchs, Henselt, Jensen, Liadov , Moskowski , Reinagle, Reinecke, Rust , Scharwenka
Post-romantic & modern:
1. Very important: Debussy, Ravel, Prokofiev, Stravinsky, Rachmaninoff, Arvo Part, Phillip Glass, John Cage, Shostakovich, Bartok, Charles Ives, Elliot Carter, Alban Berg, Schoenberg, Webern, Hindemith, Manuel de Falla, Kodaly, Messiaen, Satie. Scriabin
2.Not so important: Barber, Gershwin, D’Indy, Milhaud, Poulenc, Villa-Lobos Liapunov, MacDowell, Medtner, Reger, Richard Strauss, Arnold Bax, Lennox Berkeley, Richard Rodney Bennett, Ginastera, Britten, Dukas, Ibert, John Ireland, Monpou, Deodat de Severac, Szimanowski, Elgar, Tippet, Delius, Copland, Grainger, Griffes
3. Obscure: Gretchaninoff, Martucci, Isidore Philipp, Rebikov, Ravina, Rakov, Rietti, Rheinberger, Rosenthal, Rubinstein, Schelling, Schulz-Evler, Sinding, Sjogren, Schutt, Schyte, Stanford, Stojowski, Presner, Alexandrow, Barraud, Stanley Bate, Victor Belyi, Berezovsky, Casadesus, Casella, Castelnuovo-Tedesco, Durey, Eisler, Enesco, Samuel Feinberg, Manuel Infante, Phillipe Jarnach, Vitor Carbajo, Jolivet, Jelobinsky, Kabalevski, Charles Koechlin, Miaskowsky, Moeran, Hovhaness, Tansman, Joaquin Turina, Ernst Bloch, Paul Bowles, Paul Creston , Manuel de Ponce
By no means a complete list, just the very tip of the iceberg.

Now get googling.

Best wishes,
Bernhard.