Our common ground is just the Truth: the Dharma of Buddhism; the way things are for people and nature.
Buddhism addresses unnecessary suffering, rather than metaphysical or teleological issues such as the nature of things, or why things are as they are. Buddhism begins with the Four Noble Truths, that I paraphrase as:
Another translation of "Dukkha", rather than "suffering", is "misalignment" largely between egos versus our true or original nature. Other interpretations of Dukkha are that life is pervaded by dissatisfaction, unsatisfactory experience, anguish, and misery. These are fueled by delusions stemming from habitual discursive thinking stimulated by correlated subconscious emotions such as anger, hatred, greed, attachment, clinging, ignorance, sloth, and anxious worry, intertwined with the effects of jealousy, envy, avarice and pride.
The Four Noble Truths are a diagnosis, and the 8-Fold Path is the prescription; The Heart Sutra and the Metta Sutra also respectively diagnose and prescribe, but in more detail, about a page each. You can find these and other Sutras easily, searching by title on the web.
The Middle Way balances between the opposites of ascetic austerities and self-indulgence. "There is addiction and indulgence of sense-pleasures; and there is addiction to self-mortification, which is painful, unworthy, and unprofitable ... the Middle Path gives vision, gives knowledge, and leads to calm, to insight, to enlightenment and to Nirvana ... The Middle Path is just this Noble EIghtfold Path ... "
Other principles of Buddhism include no self (anatta), transience of experience and impermanence (anicca), emptiness (nirvana), and causation (karma). No self means simply that beings and things are interdependent and changing; independent beings and things are only imagined by our mind's thinking and used in our communications, including writing. Experience however is always changing. Impermanence means everything changes, including our egocentric notions of how things are, what this is, and who is. Emptiness defies logical interpretation; but is the truth of our experience, and even of physical energy/matter. Causation, or karma, implies that things happens due to prior causes and conditions.
Buddhist practice engenders awakening and liberation. Buddhas awaken to unsurpassed, complete, perfect enlightenment, i.e., Buddha's enlightenment. Many others experience gradual awakenings and increasing openness over the years, as well as a subtly increasing sense of transparency within ourselves and our practice, and a sense of being increasingly permeated by the sweet energies of nature, nirvana, and emptiness.
There is no single contemporary source in Buddhism. Instead most countries have separate organizations or lineages of Teachers, and they are quite diverse. Some are faith-based, like western religions. Among many notable sources the Dalai Lama (Tibet) takes kindness as the core of Buddhism and happiness as the purpose of life. But, while kindness and happiness are essential, and practice is key, there is still a great deal of Dukkha in life. Also notable, Thich Nhat Hahn (French/Vietnamese) emphasises mindfulness and practice; see my review of his book: "The Heart of Buddha's Teachings". Thich Naht Hahn's small book "Be Still and Know" includes "Peace is all around us, in the world and in nature, in our bodies and our spirits. Once we learn to touch this peace, we will be healed and transformed. It is not a matter of faith; it is a matter of practice." Peace is one Ideal among many, e.g., Truth, Love, Beauty, Compassion, Kindness, and Equanimity. Thich Naht Hahn's statement applies equally to each Ideal, and any Ideal can serve as the Ground for practice. Realizing and manifesting Ideals is approached through practice.
Buddhism is relatively free of rules and beliefs. Instead Buddha urged students to practice relying on their own experience. Practice in general can be described as what one does with respect to one's changing understandings of life's principles.
"Spiritual practice is not some kind of striving to produce enlightenment, but an expression of the enlightenment already inherent in all things" is from Eihei Dogen's book "Beyond Thinking", edited by Kazuaki Tanahashi." Just after his enlightenment and attainment of Buddha nature, Buddha purportedly said something like "it is wonderful that all things, and all beings, are enlightenment".