I live in Pasquotank County which is contiguous with Gates and Currituck. Of the 3 counties you mention, whatever you do, buy in Gates County. It's still very rural and nowhere as developed as Camden and Currituck. They are building big subdivision developments right and left in those counties. Camden and Currituck are becoming the NC extension of Chesapeake. Not so much in Gates. It's close enough to Suffolk, VA that you still have relatively convenient access to all the big box stores, etc. while being very rural. It also is going to give you the best price of the 3 counties you are looking in.
I am thinking the reason you aren't seeing larger land parcels in Camden and Currituck is the fact that they are developing so fast. The builders are buying large parcels of farm land and subdividing into 5 acre and less lots. If you are looking for country living where you can have your own range in your back yard or keep livestock, you are seriously going to want to be in Gates. My wife and I have talked about selling our land here and moving, but have to much invested and are getting too old to make a bold move like that.
I would contact a local realtor in either Elizabeth City (Pasquotank County) or Ahoskie. The latter is actually in Hertford County, but will have the bulk of listings in Gates. Realtors can be seriously helpful in that they know the area and will know about properties that may not be listed on the web.
Here's an example of a listing page of properties in Gates County. I set up the "filters" on the web page to only show properties 10 acres or more and this was the result in Gates County.
https://www.realtor.com/realestateandhomes-search/Gates-County_NC/type-single-family-home,farms-ranches,land/lot-sqft-435600