Just to get a frame of reference: How much CO2? I'd assume that building once, and then not having to replace it for hundreds of years is the long con and more energy-efficient, if that's the metric we're going by.
Even tiniest improvements in quality of building, it's heating system and insulation will result in dramatic changes. This favours something well built, well insulated, with a heatpump, high thermal mass, and most importantly with heat recovery ventilation. Not hastily constructed crap that goes to shit in 30 years.
I have not heard of any carbon capture technologies that are more efficient than trees and oceans, so the best we can do is facilitate a process that generates less CO2 from fuels spent.
So CO2 comes from the reaction between limestone and clay. And comes from burning natural gas or coal to generate the heat needed to drive the reaction.