Paul Birch sprouted a few terraforming ideas in the early 1990s that deserve more attention in such discussions IMHO.
He has an unpublished paper online which discusses some very interesting technologies for terraforming Mars and Venus. He estimates that both planets could be given breathable atmospheres in ~20 years – Venus could be cooled sufficiently to cause its atmosphere to condense in about a decade using a clever cooling technique he describes. A vast system of planet-circling hollow balls with a bit of water inside would be enough to actively cool the planet, once a sufficiently opaque soletta is in place.
But, as he notes, three planets in one system isn’t much for a growing civilization. He proposes some very elaborate and clever ultra-structures one of which answers the post title: a SupraSelf. The object is a multi-layered structure 1.2 lightyears across which has one-gee surface gravity from its own mass. In my mind it’s physically the ultimate artificial habitat until we learn how to make pocket Universes – for that idea check out Greg Egan’s story Borderguards.
A habitable object 1.2 light-years across would mass 2 trillion solar masses – twice the Milky Way. Such an object would be visible via its waste heat, but the red-shift would make it almost invisible – thus making for a hefty “Dark Matter” Galaxy. Birch says the inner layers (it is composed of 30 million nested shells) could have a red-shift/time-distortion factor of 2,500 making for some very curious possibilities indeed. Total area is ~200 billion trillion Earths – all of it inhabitable, unlike most of Earth. A population of 10^35 would be feasible. Surely a worthy effort for a Kardashev Type III to create over a few billennia.