Discography:

Rachmaninoff: Piano Concerto Number 1, as performed by Krystian Zimerman and Rachmaninoff - Piano Concerto No. 1 (Zimerman, Ozawa) - YouTube

Rachmaninoff: Aleka Evgeny Svetlanov conducts Rachmaninoff Aleko - video 1989 - YouTube

Joint Improvisations:Arensky, Rachmaninov, Glazunov & Taneyev - Four improvisations for piano - YouTube

Rachmaninoff: Piano Concerto No. 2, performed by Alexander Brailowsky with the San Francisco Symphony.

A Chronology

1873 - Rachmaninoff is born to a military family. His father is a retired officer; his mother’s father was a general.

1878 - Rachmaninoff, already displaying precocious talents, begins piano lessons at the age of 5. His parents, however, have plans to make young Sergey into an army officer also. (BritannicaSergey Rachmaninoff | Russian musician | Britannica.com)

1883 - Rachmaninoff enrolls at the St. Petersburg conservatory, aged ten. He receives poor marks.(Sergei Rachmaninoff - Tchaikovsky Research)

1885 - Rachmaninoff’s father loses the family fortune through a series of poor investments. He abandons the family. Young Sergey, at the urging of a relative, is sent to Moscow to study (and live) with the famous and famously strict piano teacher Nikolay Zverev. (BritannicaSergey Rachmaninoff | Russian musician | Britannica.com)

1888 - In addition to lessons with Zverev, Rachmaninoff enrolls in the Moscow Conservatory. He impresses his examiner, Tchaikovsky, who reportedly remarks “for him, I predict a great future,” and puts him in the classes of study with Anton Arensky and Taneyev; Taneyev especially encourages the young artist in his composition.

1889 - Rachmaninoff has a burgeoning interest in composition, and because the one piano in his teacher’s house is always occupied by practicing students, asks Nikolay Zverev to buy a second piano to support his composition. 

The Houston Symphony writes: “Evidently, he didn’t ask nicely enough because Zverev was furious (he was generally against his students composing too much anyway, since time composing was time not spent practicing piano).” (https://www.houstonsymphony.org/rachmaninoff-love/)

This incident (combined, I’d sure guess) with others, led to Rachmaninoff’s ejection from Zverev’s house. He stayed with his relatives, the Satins, while finishing his studies at the Moscow conservatory.

1892 - Tchaikovsky continues to encourage and praise young Sergey, who writes in a letter to a friend:

”Tchaikovsky said… that he would have to stop composing eventually and make way for younger people. When the reporter asked him if there really were any such young talents, Tchaikovsky answered in the affirmative and mentioned  Glazunov  for  Saint Petersburg  and me and  Arensky  for  Moscow . That made me so glad! My hearty thanks to the old man for not having forgotten about me!” Sergei Rachmaninoff - Tchaikovsky Research

Rachmaninoff begins work on a number of operas, some in collaboration with Tchaikovsky’s brother, Modest Tchaikovsky (though these are never finished). His premiere of Aleko is a real success and Tchaikovsky is thrilled by it. The Tchaikovsky Research foundation writes:

“Like the rest of the audience that evening, Tchaikovsky applauded enthusiastically at the end of the performance, and, as Rachmaninoff later recalled, he had suggested to the younger composer that Aleko should be performed together with  Iolanta  as a double-bill at the Bolshoi Theatre” Sergei Rachmaninoff - Tchaikovsky Research

Evgeny Svetlanov conducts Rachmaninoff Aleko - video 1989 - YouTube

1894 - Tchaikovsky dies, and Rachmaninoff’s family notices his first symptoms of his depression. Depression And The Composer: Rachmaninoff’s Story | Northwest Public Broadcasting

He recalls, posthumously: 

“Of all the people and artists whom I have had occasion to meet, Tchaikovsky was the most enchanting. His delicacy of spirit was unique. He was modest like all truly great men and simple as only very few are.” Sergei Rachmaninoff - Tchaikovsky Research

Sometime around here: Rachmaninoff falls in love with his cousin, Natalie Satina.

1896 - Rachmaninoff, Arensky, Glazunov, and Taneyev indulge in that memorable parlor game: joint improvisations. 

Arensky, Rachmaninov, Glazunov & Taneyev - Four improvisations for piano - YouTube

1897 - A (possibly inebriated) Glazunov conducts the disastrous premiere of Rachmaninoff’s first symphony. This was undoubtedly part of the problem, but the music was also called into question. The famed critic Cesar Cui wrote of it.

“If there were a conservatory in Hell, and if one of its talented students were to compose a programme symphony based on the story of the Ten Plagues of Egypt, and if he were to compose a symphony like Mr. Rachmaninov’s, then he would have fulfilled his task brilliantly and would delight Hell’s inhabitants. Out from the Depths of Hell: The Reception of Rachmaninoff | Music 242 – Spring 2014

Rachmaninnof’s depression worsens. He enters a three year barren period in which he cannot bear to hear his own music.

1900 - Rachmaninoff’s aunt suggests he try the psychoanalytic methods of Sigmund Freud. He begins seeing a hypnotherapist called Nicolai Dahl, who, over the course of several sessions, hypnotizes Rachmaninoff and repeats “You will write a piano concerto. It will be of the highest quality.”

It works. Rachmaninoff begins composing his Second Piano Concerto.

“Their desire to wed, however, posed some obstacles: it was against the law of the Orthodox Church, and to make matters worse, Rachmaninoff was not a regular churchgoer. Through family connections, they made arrangements to be wed at a military barracks, because barracks priests reported not to the Holy Synod, but to generals (such was the relationship between church and state in Imperial Russia). There was one last hurdle to clear, however; they had to receive permission from the Tsar during the ceremony in order for their marriage to be legal. Fortunately, the telegram came through and everything went off according to plan.” Rachmaninoff in Love: The Troubled Genesis of a Masterpiece, Part II - Houston Symphony