Better define what you mean by seaworthy - my boat doesn't leak a drop but that doesn't mean I'd want to sail it out of range of land and weather forcasts.
People on this site lean conservative - they tend to want a boat that can handle anything thrown at it if they're headed offshore. I.e. new(er) rigging if boat is used, carefully anchored chainplates, skeg-hung or keel-hung rudders, etc. You might see a lot of 30-something foot coastal cruisers in your pricerange that would be great family boats, but aren't built as conservatively.