Since the books in the Bible are not ordered chronologically, it's a matter of preference. The most important books in the Bible to study are what are called the gospels: Matthew, Mark, Luke, and John. They are accounts of the life of Jesus and his direct teaching from the perspectives of different people. Genesis starts at the beginning of everything and has relatively easy-to-read stories, so it is a good book to start with. It is valuable to read a publisher's introduction to a book before reading the book.
Genesis
John
Mark
1 John
Acts
Ephesians
Galatians
Luke
Matthew
1 Corinthians
2 Corinthians
Romans
James
1 & 2 Peter
then the rest.
Before digging into the Old Testament, get an overview of the history of the Jewish people, otherwise knowing how each book fits into the big picture will make parts of them hard to understand.
Good books to read in the Old Testament are:
Exodus
Deuteronomy
Daniel
1 Samuel
2 Samuel
1 Kings
2 Kings
Psalms
Proverbs
Isaiah
Ruth
Jonah
(Reread the gospels at some point)
You can read Nehemiah, Ezra, and Esther as a set when you get there.
then the rest.
If you want to read Psalms or Proverbs earlier than shown in the above list, consider first reading something about two of the main authors, David and Solomon (found in 1 Samuel, 2 Samuel, 1 Kings, 2 Kings, 2 Chronicles).
Skip the genealogies found in a number of the books on your first read through the Bible. (e.g., "... Rehoboam the father of Abijah, Abijah the father of Asa, Asa the father of Jehoshaphat, Jehoshaphat the father of Jehoram" etc.)