Holley Carb VS Carter Carb on six cyl?

I would avoid a parts house rebuild of either, it will be a waste of cash. Buy a rebuild kit, a couple cans of Gumout and go to town. Both the Holley 1920 and Carter BBS are about as simple as carbs get (except a Rochester B) and would be a great first rebuild. Follow the instructions in the kit, and score a Factory Service Manual if possible.

The above assumes your current carb hasn't been screwed up by some DSPO and the throttle shaft isn't sloppy loose in the throttle body.