In my previous Fantasy Garage post I touched on the enormous success of the Mustang as it related to the Mercury Cougar. I've never found Mustangs all that exciting and probably wouldn't want to own one, but I do find some of the Mustang's competition appealing. It took GM more than two years after the introduction of the Mustang to get its response, the Camaro and Firebird, to market, but in the spring of 1964 Chrysler had a small, sporty car on sale a few weeks before the debut of the Mustang.
The Plymouth Barracuda wasn't nearly as successful as the Mustang, largely because from the waist down it was still a lowly compact Valiant; a fastback roofline with a large, curved rear window were the only visual differences between it and a Valiant two-door hardtop. It was still a good move, but compared to a Mustang it wasn't going to excite anyone. (I was looking for sales figures but couldn't find them readily.)
Most people are into the beefier and more muscle-oriented 1970-74 Barracudas, but I'm not most people; I'd much rather have a 1967-'69 model, in particular a convertible. The '67-'69 styling is much more appealing to me. It's clean and trim, with none of the bloat that was coming to define the entire industry by the early 1970s.
Several of Chrysler's big V8 engines were available (some only in special packages), but I'd prefer my hypothetical car to have the plain old 318, which for '68 replaced the 273 as the smallest V8 available. It's capable of providing more than enough power for a car of this size without the penalty of horrific gas mileage. Whether for a modestly trimmed Barracuda intended for everyday driving when new or for present-day weekend cruising, the 318 would be a much more sensible engine choice.
One other cool note: in '69 Dodge and Plymouth offered an appearance package on certain models, including the Barracuda coupe, called Mod Top, which featured vinyl tops in floral patterns and matching fabric on the seats and door panels. These are quite rare but very groovy-looking.
(Top image from Wikipedia; bottom from The Truth About Cars.)