A huge ball of frozen heavy water reinforced with random carbon fibres is built from one of the ice moons, asteroids or comets. This is hollowed out, and spun to create artificial gravity on the inside surface as per your standard generation ship. The deuterium is used to drive a fusion
rocket and/or nuclear mass driver.
Ice is thus the structure, the fuel, the reaction mass, the air supply, and the rad shielding.
After reading [link 1] which shoots down the prospects for human interstellar colonization and  I propose the following.
The technical trifles which negative nellies throw in the way of our manifest destiny to populate the universe may be summed up as follows:
c/ Microgravity effects on the human organism
d/ Radiation ditto
e/ Launch costs
I leave such piffling matters as economic justification and political and public will to others.
The traditional scifi way of dealing with a/ and b/ without magic has been to build a humungous ship, fill it with lots of people and push it slowly through space as they have babies, die, etc.
This is known as a generation ship. Pushing slowly lowers the energy required, and making babies as you go buys you time.
The most promising ways of dealing with c/ and d/ seem to be c/ spinning a (large) craft to simulate ~0.3 to 0.5 G through centripetal acceleration, and d/ putting masses of Stuff between the squishy meat monkeys and all those high energy particles.
The extra Stuff required for rad shielding poses a weight problem, unless the Stuff is Stuff that is needed for other purposes. Amongst proposals I've seen are using trash, other equipment, or the fuel as absorption mass, surrounding the habitable space.
e/ is best dealt with in all serious proposals such as this by building as much Stuff as possible off-Earth.
On or below the surface of Triton , an automated deuterium enrichment plant produces heavy water. A mass driver - basically a whopping great fire hose - shoots it off the surface to a Lagrange point.
Another automated plant is deployed on a carbonaceous asteroid to create fluffy, porous carbon fibre strands. Note these are not exotic fullerene strands, just your bog standard carbon fibre. These are also mass-driven to the appropriate Lagrange point, where they collide with the steam/water/ice streaming up from Triton, and mingle randomly amongst.
There it re-freezes and coalesces under self-gravity into a huge lump of carbon-fibre Pykrete .
When said lump reaches a certain size, the Giant Space Laser and/or robots are deployed to shape it in certain ways, to whit:
Deep beneath a kilometer or so of ice, at the center of the new body, a hydrolysis plant cracks the water into oxygen and deuterium. The deuterium is used to power a fusion drive  on the surface, either inertially or magnetically contained.
Part of the helium created in the fusion reaction is captured, and mixed with the O2 to create a breathable atmosphere.
A small percentage of the energy from the fusion drive is bled off to power onboard systems.
As the core of the planetoid is consumed, it is progressively spun up to create an artificial gravity effect on the inside of the cavity thus created. This also helps to prevent collapse of the cavity due to self-gravity. This core is filled with the O2/He atmosphere.
The initial orbit of the planetoid takes it to a near Earth encounter, where the colonists board, along with any other heavy equipment needed.
The kilometer of ice provides more than adequate shielding from the hard radiation of space, as well as from the fusion drive.
Tunnels are dug from the core to observation/agriculture decks near the surface, where short visits to view the wonders of the universe (and to prevent mass solipsism) are allowed.
Coolant channels are run near the surface for the massive, fusion-powered refrigeration system needed for the Earth approach, and the slingshot orbit around the Sun. All the illegal Freon seized by the Ozone Police is sent to meet the iceship on its way to Earth. Once out of >0C space, the Freon is fed into the drive as reaction mass.
As the fusion drive consumes the bulk of the ship, the internal cavity and its atmosphere increase in size. This allows progressively more habitable space over the course of the journey, which allows the colony population to increase, rather than being strictly limited by a fixed infrastructure ceiling.
Thus you can start your journey with a minimum genetically viable population (~200) and arrive with a small nation in tow (10k-100k).
Admittedly, the radiation protection is also being consumed, but by timing this right, your distant descendants arrive at the destination star just as their vessel vanishes in a puff of steam. By then they have built their many smaller transfer craft and are decelerating towards insertion orbits around the target planet or planets.
Where they are all amazed to find their voices drop an octave.
If fusion propulsion proves a pipe dream, then one of the other proposed or existing nuclear propulsions systems  can be used.
If fullerene toughness is desired and feasible, long strands (at least, Space Elevator long) are not needed. Short, fluffy bundles of randomly varying length should do nicely.