is there a way to only keep some of the furniture when moving?

Put the furniture you want the Sims to take with them into household inventory. Then move and choose to sell furniture - you’ll keep the household inventory but nothing placed on the lot. I do that often to let my Sims keep their furniture/decor but leave appliances, plumbing, and counters so the move is a bit more realistic.

It works the vast majority of the time but I did have one time when the inventory somehow got deleted, so be sure to save before moving just in case. 🙂