Peonies symbolize wealth and good luck, so they are very good to hang at home and there is nothing taboo about them. The old man said that it is best not to hang pictures of tigers at home, especially tigers descending from the mountains, which are unlucky. There is also a taboo against hanging plum blossoms, as plum blossoms are homophonic to mold. Everything else can be hung. I have a cross-stitch of peonies, wealth and flowers blooming in my home.
As for stones, fish and water, they are all auspicious. Fish and water symbolize success and prosperity every year.