I don’t believe there are any rules anymore, maybe by chasidim. It really depends what agreements the parents make at their sit down meeting before the chasunah. We agreed to go half on the furniture with my first two mechatonim. So I told both my daughter and daughter-in-law, don’t rush wait till you find something you really love because you will be stuck with it for 30 years. B”H they both have beautiful heirloom quality bedroom sets that they both still love. One from Spain and one from Italy and we split it with the mechutanim. Other items we wound up supplying because we are in the furniture business, and some things the kid’s got second hand from family members.
My other son took most of the antique furniture pieces from his own bedroom, leaving me just the bed and desk and that has been working for them for 5 years. We found them a used dining room set and we were able to give them the chairs and dinette table.
Today Kollel couples can find furniture that others give away. There is a chessed organization that was started this year that accepts and gives furniture and appliances I believe. I can’t remember the name at the moment but I think they have a classified ad in the JP and/or the FTJTimes.