It doesn't matter where you begin. God desires for us to HIDE his Word in our hearts. Why? So we will not sin against Him (Psalm 119:11). You can use the list I have provided, an Awana book, the list in your Bible (either in the front or back), or just pick one that means something to you.
Establishing schedule of memory passages for each grade, such as the sample listed below, has several advantages.
A primary advantage is that material learned in previous years can be easily reviewed. A frequent failure in memorization is that what is learned at one point is not retained. So, apart from good mental exercise, memorization was not too beneficial.
Memorization of entire books of the Bible is also valuable, in that it helps give some extra incentive over learning isolated passages. There is a since of accomplishment in having learned an entire book of the Bible. To avoid losing interest, you would be wise to begin with the shortest books.
1 John 2:15-17
1 Thessalonians 5:15-23
1 Corinthians 13