What to send
A sunflower reads as a fresh start and stands up well to a bright room. A peony says abundance, which is the traditional housewarming sentiment.
If the move was hard — a breakup, a downsizing, leaving a place they loved — choose lavender or a lily instead. Bright yellow can land badly on someone who did not want to move.
What to write
Skip “congratulations on the new place” as the whole message. Name something about the move: how far it was, how many boxes, the fact that they did it in a weekend with a borrowed van.
If you have been there, describe one thing about the new place in the note. “The kitchen window gets the morning light” acknowledges you have actually seen it.
If you cannot visit yet
Say when you will. A date beats “we must come over sometime”, which reads as a polite nothing.