If you're looking for gas mileage and a truck, there's not much in the 60s -- 60-65 Falcon Ranchero is about it. The 60-63 has that funky early 60s look and is roomy enough. 66-67 is a good size too. The 68-71 is a bit bigger, Torino based, but still not too big, like the 72-79. 64-77 El Caminos are Chevelle based, the 78-87 Malibu based. All are a good size to work with and easy to hot-rod.
All the US trucks were big full sized jobs. You could lightly hop up a six in one ad might get as high as 20-22 mpg on the highway, keep it under 65 mph though. Anything over and aerodynamic drag jumps way up and kills mileage. I was getting 21-22 mpg under 65 with a Jeep J-10 with a six and 4 speed, but when I took a trip in a hurry and cruised at 74 mileage dropped to 10-11 mpg!! The hopped-up six would do it without struggle or complaint though.
Speaking of Jeep... the 47-65 Willys/Kaiser Jeep pickup is small and economical. About the size of the early Courier/Toyota pickups, but definitely 50s styling. They used a small four or six. I've seen them with small blocks, but it's a tight fit. A modern big four or mid size V-6 would motivate it well. 2.5L Jeep Cherokee/Dodge Dakota EFI four or the 2.5L Ranger EFI four would be great in one of those -- good power and decent gas mileage.
If you want Ford/Chevy you'll have to go late 40s/early 50s to get a small to medium sized truck. My brother's 52 Ford F-1 is a good medium size, as are other 48-56 Fords. 47-55 Chevys are a bit bigger looking, may not be much bigger or heavier.
Another great overlooked 60s truck is the 60-64 Studebaker Lark based "Champ" pickup. Basically it's a 60-64 Lark body (the Stude compact car... which would be a great hot-rod itself!) that's been cut off a bit behind the front doors and used as the cab for a pickup. Older Studebaker trucks are interesting too -- similar in size to the 40s and 50s Fords.
You could always hot-rod an early 70s Courier, Toyota, or Datsun truck. One of those with a mild small block or even a V-6 (especially a 4.3L Chevy or 4.0L Ford) would be a fun ride and do some hauling too. Look to the high teens/mid twenties for gas mileage.