Having rented a few times, we have always done it for a family vacation. So we have wanted a dining room table with enough chairs, and big enough to seat the whole group (6 to 10 people). Something that folds out or has leaves is fine.
And we have wanted at least 2 bathrooms, 3 is nice, some can be half or 3/4 baths.
And we have wanted plenty of sleeping space. Like each bedroom should have a double bed or larger, and one of those bunk beds with a twin bed over a full would be great. Or a trundle bed. Or a futon in a sunroom or office (with doors that close). Generally we are needing to sleep a certain number of people, but we don't care if it is tight. We just want people to get beds, not have to sleep on the floor, and have a modicum of privacy (ie not in living room).
In terms of other amenities, I would love a rental house that had bikes we could use! Close to airport/other public transport is nice.