Accepting Islam is not a matter of minimum or maximum conditions.
If one accepts Islam willingly one wouldn't only say the shahada, but pray and fast etc..
As abu Hanifa -as was mentioned by sheikh 'Omar 'Abdulkafy in a lesson I've attended- said to his neighbour who was [Zoroastrian][1] who loved to drink (alcohol) but intended to become a Muslim and this was his only opposition to Islam: "Become a Muslim first and we'll see".
The other day the man came and said: "I'm a Muslim, so how about alcohol?"
Abu Hanifa said: "Now you are a Muslim if you got drunk, we may apply hadd (punishment) on you!"
So being a Muslim means taking Islam as a whole not partly. Note that I doubt the attribution of the above story to abu Hanifa, but this doesn't change the lesson one could elarn from it.
A Muslim is only allowed to marry a chaste woman: Either Muslim or from among people of the book. Note that the later kind is somehow vanishing as many Christians and Jews these days can hardly be considered as such.
Assuming this woman accepted Islam she would need a Muslim guardian -as her family are neither Muslims nor from among the people of the book- for your marriage you may need an Imam who may play the role of this guardian and two witnesses and the agreement of both of you to marry each other. [1]: https://en.wikipedia.org/wiki/Majus