If the car has an original engine (not sure, it's fenced off) I'd likely keep it. If not, a 350 should drop in with little trouble and I'd use a later EFI setup, manifold for power brakes, etc.
I'm not 100% sure I'd go this way, though. I already have an old car ('71 Comet coupe, 302) that runs but needs a cosmetic refresh. We also have a '67 Mustang coupe (289) and a '66 Mustang convertible (260, IIRC) that are running and intact, but need new weatherstripping, paint, top, etc. So maybe I'll put those back into shape and go with something else.
One project I've had my eye on for a few years is a Pembleton (www.pembleton.co.uk). I like it because it doesn't need paint (the polished aluminum is awesome), it'll get good mileage and a 3-wheeler would register as a motorcycle and could be driven in carpool lanes.
Also, CV2 parts are dead cheap. A clutch is $50 and all the wear items are similarly cheap. It's a very simple vehicle, too, so most repairs could be done in an hour or two. I'd probably go for the Moto Guzzi engine variant. It'd need periodic valve adjustments, but even if the engine dies, you can get another for $700-$1,000 or so. I think one could be kept on the road for a few hundred a year in maintenance.
I'm planning to unload about $10k of stuff I don't need on eBay, which would cover the cost of a build and then some. I'll be 39 in July, so a "midlife crisis" vehicle seems like a good idea. One of these would be practical and I figure it'd be a blast to drive around. If it returned 60 MPG (as some configurations do) then I'd be able to take off on long road trips affordably. Though the Pembleton is very cool, I want one more for the experiences it'd give. The open cockpit would make the open road a more personal experience and something like this would lead to thousands of conversations. I love back roads and small towns, so I figure it'd lead to lots of experiences and stories.
