Everyone answers this question a little differently. In general, people agree that the New Testament (NT) is what to start with first. I would also include Genesis, because it has some of the narratives people have generally heard of (Adam & Eve, Noah, etc.).
The first 4 books of the NT are called the "gospels" (Matthew, Mark, Luke, John). Each of them are accounts of Jesus' time on earth from 4 different authors (whose names are the names of each book). After that is the book of Acts which is an account of some of the events around the expansion of the church after Jesus died and ascended to heaven.
After that are the books of Romans, 1 Corinthians, 2 Corinthians, and Galatians. These are dense books that have a lot of theological information in them, especially the book of Romans. However, Galatians and Romans are part of the foundation of understanding some of the basics of Christianity.
The book of Romans through the book of Philemon (13 books) are all written by the Apostle Paul (previously known as Saul), who was converted to Christianity in the book of Acts by Jesus appearing to him. They are all letters that Paul wrote to the various churches he had planted in the past (basically all Northwest and West of Israel). Some of the letters are long and some are short. Paul addresses various problems or misunderstandings that a church was having, although he also expected the letters to be read by some of the other churches in the region. Of special interest might be the book of Ephesians which is a kind of overview of "everything." Btw, 1 Timothy, 2 Timothy, and Titus were letters Paul wrote to other ministers, rather than churches.
After Paul's letters, there is the book of Hebrews (whose authorship is not clear) which is a book written to Jewish people and it explains quite a lot for those that know the ways the Jews worshiped God before Jesus came. This is a book that is difficult to understand until one is familiar with the relationship between God and the Jewish people in the OT.
Then are books from James, the brother of Jesus who was the leader of the Jerusalem church, 1 Peter and 2 Peter, which were written by Peter, one of the Apostles, then 1 John, 2 John, and 3 John which were written by the Apostle John, then Jude (written by "a bond-servant of Jesus Christ, and brother of James"), and lastly the book of Revelation which was also written by the Apostle John. Revelation contains a lot of imagery of future events and there is a lot of dispute about what various sections mean. However, the first 3 chapters and last 3 aren't so bad, and I recommend definitely reading the last 2 or 3 chapters.
The Old Testament (OT) is, in general, fairly tough to follow until you have a basic feel for the timeline of the major events that happened to the Jewish people—something worth looking into before getting into the OT. It reveals how the Jews kept rejecting God and God's response (which is why God seems harsh to some people, when it was actually people's sin that was harsh and God acting to prevent its spread as it had before the Flood and Noah's Ark).
In the OT, however, are the book of Psalms and Proverbs which stand by themselves in the sense that you can read bits and pieces of them any time you want often without having much context and understanding of other parts of the Bible. It's worth taking a glance at them to see if you would like reading bits of them every now and then.
Before reading any book, it is well worthwhile to look up an explanation of what the book is about beforehand, because it can give an orientation that helps the book make a lot more sense. An orientation will already be in Study Bibles in front of each book. Also pay attention to the first few verses in each book, because often it helps with the context such as whether the book
For reference, these are the books in the NT in order:
Matthew, Mark, Luke, John, Acts,
Romans, 1 Corinthians, 2 Corinthians, Galatians,
Ephesians, Philippians, Colossians, 1 Thessalonians, 2 Thessalonians,
1 Timothy, 2 Timothy, Titus, Philemon,
Hebrews, James, 1 Peter, 2 Peter,
1 John, 2 John, 3 John, Jude, Revelation
All Scripture is God-breathed and is useful for teaching, rebuking, correcting and training in righteousness, (bold mine, 2 Timothy 3:16, 1984 NIV)
Above all, you must understand that no prophecy of Scripture came about by the prophet’s own interpretation. For prophecy never had its origin in the will of man, but men spoke from God as they were carried along by the Holy Spirit. (2 Peter 1:20-21, 1984 NIV)
It just means He is steadfast like a rock. Blessings.
