salam alaykum...
sister in Allah....
It is better, and is mustahabb, to do wudoo’ before reciting, because this Qur’aan is the Word of Allaah. So it is better to do wudoo’ before reading it as a sign of respect. But touching the Mus-haf is not permissible unless one has done wudoo’, because Allaah says (interpretation of the meaning):
“Which (that Book with Allaah) none can touch but the purified”
[al-Waaqi’ah 56:79]
(Majmoo’ Fataawa al-Shaykh Ibn Baaz, 10/150)
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With regard to reading or reciting Qur’aan, there is nothing wrong with reciting from memory even if you do not have wudoo’, except in the case of janaabah (impurity following sexual activity), in which case you should not read until you have done ghusl. But you should not touch the Mus-haf unless you are pure from both major and minor impurity, unless the problem is continual, in which case you should do wudoo’ at the time for each prayer, and read Qur’aan from the Mus-haf and recite from memory, because of the rulings on prayer referred to above
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<wasalam Alaykum>