There is, in fact, no difference in the Quran where you start. Understanding the whole Quran correctly, and in context is more important. If one is a serious seeker of truth, God himself will help you to understand and, then if one denies truth when they see it, God makes one unable understand the rest of the Quran and lose interest in continuing to read the Quran.
It all depends on the level of honesty of the reader in accepting truth even it is costly for him/her. For example, if one does not accept the Quran because he loves wine and then the Quran tells them to leave wine, he forgets the Quran because he loves wine more than the quran; he is not honest in accepting truth and so God puts some spiritual curtain between him and the Quran, so that they cannot be guided as punishment.
There are some hadith saying that the Quran has 70 deptha and each depth has 70 depths (each dept means a level of knowledge and meaning)
Further more the Quran says:
لَّا يَمَسُّهُ إِلَّا الْمُطَهَّرُونَ
Which none shall touch but those who are clean.
This can be interpreted to mean no one can reach deep meanings of Quran unless they purify his heart from immoralities. (for example loving wine is considered morally evil or having any prejudice about Islam before doing enough research)
خَتَمَ اللَّـهُ عَلَى قُلُوبِهِمْ وَعَلَى سَمْعِهِمْ وَعَلَى
أَبْصَارِهِمْ غِشَاوَةٌ وَلَهُمْ عَذَابٌ عَظِيمٌ
Allah hath set a seal on their hearts and on their hearing, and on
their eyes is a veil; great is the penalty they (incur).
Still, if a suggestion for a starting place is needed, I would recommend the chapter Mariya a.s.