Question about buying Carter BBD for my 318 (unless I should look at something else)

The other type has a raised box around the accelerator pump so you really can't see it, and a LOT of ports that I'd have to plug. I'm assuming the carb with a lot of ports is a more recent design? Does it perform better? (Performance, as in getting the air/fuel mixture right, especially when idling, MPG, etc).
Yes and no
The later design is better but-um will likely run too lean on your 67. Some of the extra ports will not be applicable in your application, but could be used to advantage.

But if your 1967/56yearold engine is having an Idle issue, it may or may-not be a carb-issue. I would start with a compression test, a cylinder ballance test, and if those are up to snuff, then an ignition system diagnostic/tune-up