i have a 53 buick with a straight 8, when i touch the gas lightly it skips and backfires a little, but when i push the peddle to the floor it sounds fine, now when i drive in third gear (its a three on the tree) it has no power.
Might have a little crud built up in the idle/transition circuit in the carb. I had a '78 Chevy 6 that did that pretty regularly, but a tank of Mobil Super or a dose of Berryman's Injector Cleaner in the tank always took care of it.
Straight 8 Buicks were fairly horsey running mills. I would definitely be looking at the ignition system, checking the points , etc. Check the basics of timing, point dwell, spark plug condition, and cranking compression. If you get all of that lined out, you can maybe delve into the carburetor also. Can't be too big of a deal to figure out. They don't get much simpler than an old Buick 8.