A friend of mine had some cards he was using to memorize Bible verses. In it he had Romans 12:1 and 2 from the New English Bible (NEB) translation. I love the way the NEB has translated these verses.
Therefore, my brothers, I implore you by God's mercy to offer your very selves to him; a living sacrifice, dedicated and fit for his acceptance, the worship offered by mind and heart.
Discerning God's Will
Adapt yourselves no longer to the pattern of this present world, but let your minds be remade and your whole nature thus transformed. Then you will be able to discern the will of God, and to know what is good, acceptable, and perfect.
I like using the Navigators method of memorizing verses in which you give each verse a title to help you recall it. That is why I added titles to the two verses above.
Here's a Navigators suggestion I found helpful.
When memorizing and practicing verses, recite the following:
Reference (Book chapter:verse),
This helps us to recall the verse by the reference or the words.
Here is a short article from the Navigators on How to Memorize Scripture.
The Navigators also have some suggested verses to start memorizing.
"Why memorize Bible verses?", you may ask. The Discipleship Journal magazine archives has an article (registration required) called "Verses ‘R' Us: Eight Reasons Why Scripture Memory Isn't Just For Kids".
The sub-title is "Memorizing God's Word gives the Holy Spirit the power to lead, guide, challenge, and instruct us", which is a pretty good reason to start with.