I want to know the original quotes by the Buddha and their sources.
Of course the Buddha wouldn't have used the word "reincarnation" because that's English (we've been talking on Meta recently about some difficulties translating Buddhist vocabulary into English).
This article, Buddhism and Death, says,
We can thus make a clear distinction between the terms "Reincarnation" and "Rebirth."
"Reincarnation" is the term used by those who hold that a real entity (a "soul") exists and passes on from life to life, occupying successive bodies.
Buddhism is more or less antithetical to the doctrine of a soul (it teaches Anatta), and so "rebirth" is a more usual translation than "reincarnation", of "what the Buddha said".
Then, searching for rebirth instead of reincarnation, you can find many suttas which mention "rebirth" -- for example using this search of the Access to Insight web site (on that page, click on "suttas" instead of "All results") ... that search seems to return nearly 400 suttas ... and I hope that's an answer to your question?
Access to Insight hosts translations of many but not all of the suttas in the Pali canon.
These sources are the "suttas" of the "Pali canon (Wikipedia)".
Additionally, note too that there are more than 100 topics tagged rebirth on this site (many more than are tagged 'reincarnation').
Not that I endorse this article, Buddha: Proof of Reincarnation per se, but it seems to mention quite a few of the original quotes by the Buddha and their sources/suttas.
Extracts with quotes
The Majjhima Nikaya and the Anguttara Nikaya make incidental references to some of the past lives of the Buddha.
In the Ghatikara Sutta the Buddha relates to the Venerable Ananda that he was born as Jotipala, in the time of the Buddha Kassapa, his immediate predecessor. The Anathapindikovada Sutta describes a nocturnal visit of Anathapindika to the Buddha, immediately after his rebirth as a Deva. In the Anguttara Nikaya,' the Buddha alludes to a past birth as Pacetana the wheelwright. In the samyutta Nikaya the Buddha cites the names of some Buddha's who preceded him. An unusual direct reference to departed ones appears in the Parinibbana Sutta. The Venerable Ananda desired to know from the Buddha the future state of several persons who had died in a particular village. The Buddha patiently described their destinies. Such instances could easily be multiplied from the Tipitaka to show that the Buddha did expound the doctrine of rebirth as a "verifiable truth." Following the Buddha's instructions, his disciples also developed this retro-cognitive knowledge and were able to read a limited, though vast, number of their past lives.
The Pali Jatakas record 357 past lives as a human, 66 as a god, and 123 as an animal.
The Jatakas is a collection of "birth stories" detailing many of the previous lives of the Buddha. Buddha Shakyamuni spent many lifetimes in the six realms of transmigration. His lives as the monkey king, elephant king, deer king, and goose king are examples of lives spent in the realm of animals.
The Buddha said, herein: "
Many lives ago in the past, in a city called Varanasi, there lived a man by the name of Pure Eyes (Vimalanetra) who was in the performing arts business of acting and singing" (equivalent to today's actor). "At that time, there was a beautiful woman by the name of Deer Form. Pure Eyes and Deer Form entered into a sexual liaison with each other.
"Since Deer Form was a very wealthy lady, Pure Eyes later murdered her for her money and buried her body in the house of a realized spiritual cultivator by the name of Joyful and Spontaneous Solitary-buddha.
"Joyful and Spontaneous Solitary-buddha was mistaken to be the murderer. He was tied to the back of a donkey and publicly paraded through the streets. "Just as Joyful and Spontaneous Solitary-buddha was about to be executed by arrow, Pure Eyes gave in to his conscience and confessed the crime to the prosecutor. A new investigation established Pure Eyes' guilt. Pure Eyes was executed by arrow and then beheaded."
On the very night of his enlightenment, during the first watch, the Buddha developed retro-cognitive knowledge which enabled him to read his past lives. "I recalled," he declares,
"My varied lot in former existences follows: first one life, then two lives, then three, four, five, ten, then a hundred, a thousand, a hundred watch the Buddha, with clairvoyant vision he perceived beings disappearing from one state of existence and reappearing in another. He beheld the "base and the noble, the beautiful and the ugly, the happy and the miserable, passing according to their deeds."'
These are the very first utterances of the Buddha regarding the question of rebirth.
In his first paean of joy, the Buddha says:
"Through many a birth wandered I, seeking the builder of this house. Sorrow full indeed is birth again and again."
In the Dhammacakka Sutta, his very first discourse, the Buddha, commenting on the second noble truth, states: "This very raving is that which leads to rebirth." The Buddha concludes this discourse with the words:
"This is my last birth. Now there is no more rebirth."
The Majjima Nikaya relates that when the Buddha, out of, compassion for beings, surveyed the world with his Buddha-vision before he decided to teach the Dhamma, he perceived beings, who, with fear, view evil and a world beyond.
Maybe Mr/Mrs Wally likes to start with "The Truth of Rebirth: And Why it Matters for Buddhist Practice". Its based on the Buddhas Leagcy and leads - in a direct way, without holding something back - to them in detail.
(Note: this answer has not been given with the agreement to be means of trade or the purpose of/for trade and/or keep people trapped and bound. How you handle it lies in your sphere, but does not excuse the deed here either.)