No, mainiac, I'm talking about the large-scale interstellar travel. It's a lot easier to carve a colony out of a chunk of rock and move that chunk of rock than construct a ship the size of the chunk of rock and have it move. And I'm not talking about "most practical" or "most feasible", but "best". There is no better way to travel in space than on the planet you're inhabiting. Setting it up to be able to travel is another thing entirely, and I did say non-newtonian engines. By the time the sun's about to go blow on us, we just might have a technologically feasible way to take our planet off its orbit and fly away into the wild green yonder.
Moving the earth (or even mars, altough it´s half as large) would be impractical, since you're dragging around an ungodly amount of dead weight. Basicly, you only want to have the bare neceseties, like beams for structural integrety, a surface to mount things on and shielding to keep air in and nasty radiation out. Everything else you'd be dragging around is just stuff that's not helping but does need acceleration. Therefor it'd be
Many Many Many times easier to carve a ship out of an asteroid then to move a planet, but then you're not realy talking about a planetship anymore. (of course I could go off in a tangent and say a Dysonsphere would be even more efficient, but we´re already too far away from our current reality'. Of course if you´re also using the excess mass as fuell it´d be another thing entirely, but then you´d need to make sure that the extra mass and extra thrust scale apropriately.
One thing to take into acoutn when talking about a moving colony is that it´s in the end an open system. There´s no way you can cheat thermodynamics, so you´ll always have the problem that you´re generating entropy at quite a fast rate. On earth that is compensated by work delivered in the form of radiation energy (mainly light and infrared), but once you leave our solar system, you'll need to take some sort of energy with you instead. You proposed brining a replacement sun. I'd keep things a bit smaller, but nuclear fusion is certanly an option, especialy when using a large-scale electromagnetic "scoop" to suck in hydrogen attoms from the surrounding space. But another option would be to prefabricate and store enough energy to get to the next star and recharge there. Tests have shown that thermal energy stored in molten salt only decreases with 1% per year, and that's with our current methodes to keep something adiabatic. presumably, you'd get a bonus if packing in large volumes (less contact area relative to the energy stored), and isolation would also improve. Storing electrical energy would be harder though, but perhaps it can be stored in the form of chemical energy. Superconducting coils would also be an option, but current desing only go up in the terrajoule range (which is practicaly nothing compared to our current anual energy usage), and they have a loss of aproximately 40% over longer periods of time, and are only desinged for a few days of operation. They're a lot more efficient then batteries though