I like the Dalai Lama, Pema Chödrön, and Thich Nhat Hanh. The Dalai Lama has some great introductory books. He is more modern than his predecessors, yet he is the equivalent of the Pope regarding Tibetan Buddism, so his modernizations are actually canon. Pema Chödrön is a Canadian woman whose life changed in her 40s in a very painful way. She took much comfort from the teachings of Chögyam Trungpa, who is a pre-eminent Vietnamese Buddhist. Thich Nhat Hanh is very popular and for good reason. He teaches ways to find calm in the midst of turmoil.
Friends of mine have gone deeply into Japanese Buddhism, but I find myself arguing with it too much. Caeli recommended some books on Theravada Buddism, which is Sri Lankan. Theravada is the tradition with a capital T. They are the oldest texts. The Lotus Sutra is considered the core text, and you can even find a translation by Henry David Thoreau that was published in Ralph Waldo Emerson's magazine, The Dial. I mention this to give you a sense that, in America at least, interest in traditional Buddhism goes very far back and is ingrained in what has become our classical literature.
In general, the difference between Buddhism and Hinduism is that Buddhists do not believe in God. Hindi, however, call God a variety of names yet they believe that all the names are really for a singular being, Vishnu, of who Krishna is the supreme persona. But Buddhists don't believe that. Buddhists and Hindi both meditate a lot, but while the Hindi bask in the presence of Krishna (it's called Bhakti yoga), the Buddhists clear their minds of anything they consider illusion, which to them includes all personifications of divinity. Both seek unity with the All, but the Hindi consider the All to be a person. Both practice compassion, but while the Hindi believe they are purging themselves of the effects of bad karma, the Buddhists admit to a purely selfish reason for their compassion; it eases their own suffering.
Anyhow, one inroad is to read Pema Chödrön When Things Fall Apart. It documents her own learning and has a lot of life advice that will stay with you a long time.