What book in the Bible should I read first so as not to get lost or give up?
In the Old Testament, you may want to start with the Book of Exodus (God leading the Hebrew people out of Egypt, making a covenant with them, and guiding them into a new land). In fact, one verse after the crossing of the Red Sea (15:21) is regarded by some scholars as the oldest text in the Bible.
In the New Testament, you could start with the Gospel of Luke, which has given us angels and shepherds at the birth of Jesus, several of the most well-known parables (prodigal son and the good Samaritan, for example), Jesus appearing to two disciples on the road to Emmaus, and the commission that the disciples preach to all nations repentance for the forgiveness of sins.
I recommend that you read a translation that has good introductions to each book and cross-references to other biblical texts (perhaps for a second reading of these texts). The New American Bible and the New Revised Standard Version are very readable English translations and have the introductions and cross-references recommended above. You can “own” the Bible in a legal sense, but its real ownership belongs to God and the faith community that recognizes it as God’s unique self-revelation.
Please remember that you are not reading court transcripts but rather faith accounts: God’s revelation conveyed via human words. If you get bogged down or discouraged at some point, you might take a break and explore the treasures in the Book of Psalms; there is at least one psalm that reflects the human mood you are feeling then.