Pure Oxygen at 0.2 to 0.3 atm
When terraforming a planet the terraformers must make one major choice. Go for a 100% terraformed planet and pay 100% of the cost in time and resources or go 95% of the way and pay 1% of the cost. This answer assumes that the terraformers choose the second approach and that the moon will require further maintenance to remain habitable.
The O2 will be produced by cooking it out of the luna lithosphere. After all, a big part of the moon is oxygen bound in rocks. Solar, nuclear or fusion powered furnaces will do the job. The oxygen will escape into space over thousands or millions of years and will be used up by the luna surface. The luna rocks are a chemically reducing environment and must be saturated with oxygen first to be come an oxydised, earthlike one. This also happened on Earth and is the reason why historic oxygen records never surpassed 5% for a long time and how banded iron formations got going. The low pressure is all humans need, just look at what the Apollo program used in the capsules.
Co2 will be needed in low concentrations for plants. Just import it, or really just the carbon as you got a lot of oxygen on hand.
Water Vapor (H2O) is required anyway for a habitable world. You could move enormous masses of water in the form of brutally impacting comets to Luna, rendering it uninhabitable until the water transport is complete. Or you could just import the hydrogen as it is way more mass efficienct and cheaper. Hydrogen should be sourced from Saturn and the ice-giants. Water vapor is needed for the atmospere as dry air is bad for living organisms. I would recommend going for large, shallow oceans not deeper than a tens of meters. This will get you the moisture you want for weather as much as deeper oceans would.
Nitrogen (N2) is a tricky one. It is needed for planets, but not in huge quantities and not really in the air. As it can only be sourced from Titan, Venus or Earth, taking large quantities from any of these places might ruffle a lot of feathers. Just import small quantities and give it to the plants as fertiliser.
All the gases we need will escape slowly. So the inhabitants of Luna will have to replace their atmosphere constantly, but this won't be an issue and there really isn't a way around it. Unless you are willing to spend hilarious ammounts of energy to oxydise the entire surface and are willing to dome Luna over that is. This would be how to handle the oxygen issue. The other relevant gases must be shipped in regularly in the required quantities.