I think the Whitehouse “historian” or whoever it is that checks for the appropriateness and accuracy chooses several styles, and then the First Lady chooses one.
I don’t think the First Lady begins a search at random and chooses.
Interesting, this photo from today’d Dairy Mail shows the cane of the Oval office table, carpet and sofa.
I’ve always hated the Obama sofa which was a holdover from the Bushes:
http://www.dailymail.co.uk/news/article-4633790/Trump-spent-twice-Obama-spent-furnishings.html
Thanks.