It is a general tendency to collect articles, read, and then write the review. In my personal experience, I would suggest putting the writing part second because if we wait till we finish reading, it would delay the whole process. Another key aspect is to understand the gist of the papers, see if there are contradicting findings and if there are contradictions, make a decision as to which one is a more reliable finding. All these considering that it is a comprehensive review.
When I was close to finishing a review article about a year back, I stumbled upon this blog. I hope this will help.