What is beneficial for one person may be different from what is beneficial from another. However, my own thought is that it may be good to start from the middle of the Qur'an (really you could just open it to the middle and see what catches your eye). The reason for this is that the earlier surahs contain more passages related to the historical situation of the Muslim community at the time, and the later surahs contain more metaphorical language.
If you have a particular interest in the story of Jesus or the Virgin Mary in the Qur'an, you could also start with Surah Maryam (Surah 19) and Surah Al-i Imran (Surah 3), although you should keep in mind that these surahs cover other topics as well.
You could also consider starting with the following surahs:
* Surah Yusuf (12), which contains the Qur'anic treatment of the story of Joseph and is strongly focused on that narrative.
* Surah al-Qasas (28), which discusses Moses and Pharaoh
* Surah al-Kahf (18), which tells of the seven sleepers of the cave
These might be good choices to start with because they are strongly narrative-focused and there is shared material between the Christian and Islamic traditions, although there are some differences in the Qur'anic treatment of these narratives.
In any case, the most important thing is to have a good translation. I have been very impressed by _The Study Qur'an_, ed. S. H. Nasr. It is the best translation I have seen, and also has excellent footnotes. It is a bit heavy due to the essays in it, but one should not be intimidated because the actual text of the Qur'an is not that long.
Happy reading! If you have specific questions on specific verses, you could ask here.