An idea of the core teachings of Buddha can be derived from the Maha Parinibbana Sutta...the teachings before his final nibbana.
In the sutta, the Blessed One says,
"Now, O bhikkhus, I say to you that these teachings of which I have direct knowledge and which I have made known to you — these you should thoroughly learn, cultivate, develop, and frequently practice, that the life of purity may be established and may long endure, for the welfare and happiness of the multitude, out of compassion for the world, for the benefit, well being, and happiness of gods and men.
"And what, bhikkhus, are these teachings? They are the four foundations of mindfulness, the four right efforts, the four constituents of psychic power, the five faculties, the five powers, the seven factors of enlightenment, and the Noble Eightfold Path. These, bhikkhus, are the teachings of which I have direct knowledge, which I have made known to you, and which you should thoroughly learn, cultivate, develop, and frequently practice, that the life of purity may be established and may long endure, for the welfare and happiness of the multitude, out of compassion for the world, for the benefit, well being, and happiness of gods and men."
Thus, one sees that Buddha directly exhorts the Sangha to thoroughly learn, cultivate, develop and frequently practice the following teachings for the benefit of oneself and many:
- The Four Foundations of Mindfulness
- The Four Right Exertions
- The Four Bases of Power
- The Five Faculties
- The Five Powers
- The Seven Factors of Enlightenment
- The Noble Eightfold Path
These 37 factors are together called as the BodhiPakkhiyaDhamma or 37 factors of Enlightenment.
Now coming to this comment,
You can find the core teachings of Jesus by reading the Bible, There is no Buddhist Bible. Im so far unable to find a english Pali Canon to read.
To me when people say I must have a tradition to know what the teacher says its like saying you can't explain jesus's teachings cause its to hard with out traditions. You dont have to be catholic, Methodist, Lutheran, Evangelicalism, or even Baptist to simply look up the text an see for your self what he taught, without the dogmas and doctrines to keep you ensnared into a rigid form of the faith an blind to what it means. This examples shows how some traditions an customs keep you from the truth an keep you distracted away from the teachings.
I think, in general when people urge somebody to adopt a tradition, it is because there is a great deal of emphasis on meditation in Buddhism. Without meditation one might know things intellectually but not experientially. For meditation, one might attend a retreat nearby. Dhamma.org - link for 10 day course registration at one of many centres in the world is a great option.
As regards the right teacher and right tradition for oneself, the Kalama Sutta provides great guidance. Herein the Enlightened One says,
'Don't go by reports, by legends, by traditions, by scripture, by logical conjecture, by inference, by analogies, by agreement through pondering views, by probability, or by the thought, "This contemplative is our teacher." When you know for yourselves that, "These qualities are unskillful; these qualities are blameworthy; these qualities are criticized by the wise; these qualities, when adopted & carried out, lead to harm & to suffering" — then you should abandon them.'
"Now, Kalamas, don't go by reports, by legends, by traditions, by scripture, by logical conjecture, by inference, by analogies, by agreement through pondering views, by probability, or by the thought, 'This contemplative is our teacher.' When you know for yourselves that, 'These qualities are skillful; these qualities are blameless; these qualities are praised by the wise; these qualities, when adopted & carried out, lead to welfare & to happiness' — then you should enter & remain in them.