For me, it would be a toss-up:
Between a 1954 Hudson Commodore Convertible - Keep the frame but replace the engine with an engine and 6-speed auto from a later Vette and run a Jag independent rear end. Spiff the interior and add A/C and a color contrasting convertible top.
If not that, then I kinda like the Bugatti Atlantic clones I've seen (both of them) and while they are pretty, I just don't know.... Either this (same 'Vette Upgrades):
Or maybe a Delahaye, brought up to a present drivetrain:
Yeah....... The Dalahaye would prob'ly be my Fave.
Even if they just handled "OK" (and you know I wouldn't stand for that and improve the suspension if necessary), they would be worth having just to look at them!