A family of 4 will want one of the heaviest duty higher payload rigs. At least 2000 lbs of payload. I needed a typical today 2500 back in the day with a family of 6 pulling a trailer of this size. I had a 9200 gvwr K3500, empty was 6600 lbs, loaded with family, dogs, bikes, hitch weight, generator some times....truck gvw was 9000-9500 lbs, trailer axels were in the 6-6500 range.
The kids may/will want to bring a friend, so the op may end up a family of 6.....
So no, a 25 series truck is not overkill! from a payload perspective.
Marty