There are quite a few nice, traditional with good headroom 25 to 27 footers that should be available under $10K-12K and which should meet your goals. My favorite in this category would be the Tartan 27 which is a keel centerboarder. The short list might include: Longer keel boats with attached rudders like the Albin Vegas (27 feet), Bristol 27, Chris Craft Capri (26 feet), Pacific Dolphin (24), Pearson Ariel (26), Rhodes Ranger (26 feet, and not to be mistaken for a Ranger 26)
Or older fin keel boats like C&C 25, Cal 2-27, Chis Craft Pawnee (26 feet, I have never been below on the Pawnee so I am not sure about headroom), Contest 25 (which was the first boat that my family owned when I was 12 or so and my brother was 8 1/2), Ericson 27,
And more modern designs like the: C&C 24 & 26, Pearson 26, Paceship 26 (this is a real nice boat that was also sold as an AMF PS26), Northstar 26 (also called a Northstar Islander), Ranger 26, Tartan 26 (if you can find one with the cruising interior meaning with a Vee berth forward)
All of these are well rounded boats for their era. They offer a wide range of accomodations and speed but all offer good sailing characteristics and should be suitable for a first boat for a family of 4.
One minor point, I in no way meant to put down the Centaur. These are good boats for their era. My points were really directed at the issue of price relative to other boats from that era. There was a fin keel and bilge keel version of this boat. If you have a choice I would suggest that the fin keel version would have better performance and more stability. Back in the late 1960''s I taught sailing at a sailing school that used a 25 foot Westerly what I believe was probably the predecessor to the Centaur. We had both fin and bilge keel versions and the bilge keelers were inferior on all counts; motion comfort, leeway and pointing ability, and speed.
Good hunting,
Jeff