If you want a basic wire axle build, the AMT '63 Galaxie, '64 Galaxie Modified, and '64 Mercury all are good donors for typical '60s detail.

As noted by Dave, for much greater detail, the Mueller era '60 Starliner is the no-brainer of the bunch, but needs more fab work.

IIRC, a back issue of Car Modeler (wayyyyyyy back) had an article on building more detail into the '61, but it was so long ago, I'd have to start from the beginning to chase it down. Excellent coverage, though, some really smart solitions.