"The garden is the last luxury of our days, because it demands that, which is the most precious for our society: time, affection and space“

no need for the first two commas...
"The garden is the last luxury of our days because it demands that which is the most precious for our society: time, affection and space“

or...
"The garden is the last luxury of our days because it demands things most precious for our society: time, affection and space“

I like the last wording best - Ok for translating a quote?