We don't believe in the trinity. We believe in the Godhead. God the Father, Jesus Christ, and the Holy Spirit are three separate beings. Father and Son have glorified bodies of flesh and bone. The Holy Ghost does not. His body is one of spirit matter.
This is one reason why Joseph Smith's first vision is so crucial to the LDS belief system. He saw God and Jesus standing separately and in bodily form, thus revealing the true nature of God.
Of course most of Christianity differs in their beliefs about the nature of God. The Trinity is one such belief and is found in many protestant belief systems and is basically the idea that the F, S, and HG are one person that changes form. So Jesus and the Father are seen as the same being.
Others I am sure can describe the Trinity better than I. I believe the origins of the Trinity doctrine comes from conclusions made by theologians at the Council of Nicea and is called the Nicean Creed.
And one thought about reading the book of Mormon. I really like the advice of UTcowboy. I wonder if you just read a few key doctrinal chapters or a few key bofm stories. The missionaries often have people read certain sections and kinda build from there. It might be less daunting than tackling the who thing at once.
The missionaries (at least they used to. I am revealing my age here.
) would recommend reading the Introduction to the book. It contains a brief description of what the book is and the story of the First Vision and the visit of the angel Moroni and how he appeared to Joseph and told him about the ancient record. You could then read 3 Nephi 11 where Christ comes to America and perhaps the last chapter of Moroni.