I would recommend a great book titled Reading Scripture as the Word of God by George Martin. But I’ll sum up some of his points and recommendations for you.
Where to Begin - This kind of depends on how much you already know and are familiar with the Bible. If you’re just beginning, I would recommend starting in the New Testament. Read Luke and Acts of the Apostles (since the two are like two volumes of the same book - written by same author). This will help you understand Jesus’ life and the works of the apostles after the resurrection. John’s Gospel and letters are also a great place to start.
Where Not to Begin - Revelation (leave the studying of this book until you feel comfortable with the rest of the Bible). Leviticus (although very interesting the more you get into Biblical studies, it is very dry and confusing for someone just beginning).
Generally, for starting your studies you want to get a basic feel of the Bible. Don’t worry about memorizing every chapter and verse, just try to get the “big picture” for now. If a particular verse stands out to you, jot it down! Once you feel comfortable with the New Testament, begin working on the Old Testament (starting with Genesis) and basically do the same (get a general feel). This is a learning process so don’t get discouraged if it takes time - you won’t become a Biblical expert over night! I would encourage a set amount of time reading the Bible each day - start with 15 minutes. There will be days you feel like reading more than that - so do it. But there will be days you don’t feel like reading at all - it’s very important you read on those days so you don’t break the habit.
Lectio Divina is great and I would highly recommend that form of prayer. I don’t know how helpful it will be in the area of studies or scholarship, but it definitely draws you back to praying with the Bible. Trust me, it is very easy to get lost studying the Bible that you forget to pray with the Bible as well! Never abandon prayer for study - prayer must always come first!!!
One final note, it may be helpful for you to outline a certain book of the Bible. In other words, write on a sheet of paper: Matthew 1-2 Infancy Narrative. Matthew 3-7 Proclamation of the Kingdom. Matthew 8-11 Ministry in Galilee. etc.
I feel like Christ is calling me to enter the Scriptures more deeply and I really don’t know how to start. Do I start at the beginning and work my way through? Start with the Gospels? Open to a random page? I would like (eventually) to be able to quote chapter and verse… Does that just come with time or is there a certain technique?