You have not said new or used and you have not said a price but let me gamble anyway. I think you want to set your low end at 32 and high at 38 feet for this move. It knocks out quite a bit but centers more on the likely. Below 32 is less comfortable for a family - yes you can do it but why not get it right? above 38 and you start down the trail of a full time liveaboard so this is overkill for your needs. I like diesel but gassers are more common and cheaper to buy under 38. Because I have Bayliner I can say there are several models (motoryacht not express) of used in that size range that should come in from $15,000 to $50,000 They all have a lot of bang for the buck.
Here is a 32 diesell at $29,000 in Florida
1986 Bayliner 3270 Diesel Power Boat For Sale - www.yachtworld.com
I have seen gassers go at under $10,000
I have no financial interest in nor can I speak for the actual quality of any specific boat, but I can say these types are worth a look.
There are also numerous other brands which may be set up for a planing hull but can be run as a trawler with close to trawler efficiency
Here is a gas Mainship at under $25
1988 Mainship Aft CAbin Power Boat For Sale - www.yachtworld.com
Here is a very pretty Albin at $39
1988 Albin 34 Aft Cabin Power Boat For Sale - www.yachtworld.com
Anyway - you are in great boat country and lots of choices around you - take the family and get on a few of these - good luck