I suspect the major problem with terraforming Luna would be soil chemistry, and soil properties in general.Well technically, a terraformed planet or moon wouldn't look anything like it used to unless you reshaped it to so all the craters of the moon would be eroded under the colossal amounts of heat and energy in terraforming and then eroded further by the new atmosphere and sea.
You could probably set the climate of the moon to whatever you wanted it to be after terraforming and it would be plenty plausible.
The materials in the surface rocks differ from Terran ones in ways that might interact badly with Terran evolved life forms. Mind, life is pretty resiiliant, so I suppose if we just did a quick dirty job, dumping the necessary masses of mitigating minerals on the surface, then dumping on atmospheric gas and water to taste, and seeded it with basic bacteria then eggs of the various worms, bugs, and fungi that form the biomatter of soil with a scattering of some tough colonizing plant seeds, then genetically engineered some organisms on various scales to turn the dirt over, something would survive any imbalances, and the way to get good results in this respect would be to step away for many millions or tens of millions of years and let the organisms adapt. Trouble with that is that while a rich and stable suite of ecosystems will form, they might not be very compatible with Terran life as we like it.
Meanwhile--Lunar grit on all scales has undergone no polishing by air or water erosion whatsoever. All the surfaces are jagged. Inhaling raw moondust would do terrible damage to human lungs. Again if we were to dump on an atmosphere and hydrosphere and step away for many millions of years, gradually everything will converge toward Terran type conditions . But if we are thinking of settling the Moon very quickly, in just hundreds of years, lunar regolith would have to be painstakingly processed in some kind of polishing process quite a lot, before we think about adding adjusting minerals and biomatter and working it into proper soil.
I suspect it is more realistic to gradually cover the moon with dome colonies, where the floor of the habitable volume is glassed and then sealed off, and exterior regolith is carefully polished into acceptably smooth particles, and adjusted piecemeal to layer the ground inside the dome. Or of course we just dig into the rock, being very careful with the dust we generate in vacuum, and seal off the walls, and create terrarium chambers as we please, for decorative or functional purposes.
There is also the gravity issue. I think it might be practical to lay out banked railroad tracks for a 1 kilometer radius circle, and run a train around it fast enough for the cars to be at a full Earth G, rolling along in vacuum in tunnels providing sufficient radiation shielding, with shuttle cars that can sidle up and lock to one of the moving cars, and then separate and take a switch to brake down to a stop. The circular tract of surface inside the circle will be leveled, smoothed, covered over with sealant, domed over and soil created to cover the interior for a combination of useful photosynthetic plant action and human recreation. But people would generally have to spend a lot of time on the high-G train cars.