OK. I made one "typo" (well, "though-o"). I mean fission power, rather than fusion, would be enough to get us out to the Oort clouds.
OTOH, the icy moons of Jupiter have too high a gravity to be an attractive choice. You'd need specially designed equipment. Those are no minor masses. Still, there are plenty of icy asteroids beyond Jupiter's orbit.
WRT the Oort clouds...there's a lot of stuff there, but it's rather thinly spread. So figure long transition times between "stops". Probably not practical until we are building habitats the size of cities.
For that matter, it's not wise to focus too tightly on one particular approach. Consider a habitat that's in the shape of a long tube, and that grows by building onto the ends. Perhaps a couple of miles in diameter, though different sections could have different diameters. And spinning, for gravity. Given a long enough tube you can make bends through some pretty sharp angles without causing much stress, though I would design it so that different sections could be safely decoupled, and replaced, removed, or inserted.You'd probably want an occasional non-rotating section. Transport if via electric train, though, so you'd want the sections to be pretty long, to avoid excessive transfers, unless you run the trains in an evacuated tube in the center. Occasionally you'd want an extension to run either straight in or straight out. Power collected at locations near the sun. How far could you find building material to reach? Now use one of the "straight out" constructs as a linear accelerator to launch vehicles to the stars. You should easily have an accelerator 100's of miles long in a vacuum all the way. I'd be a bit hesitatnt, however, about using it to catch incoming freight, even presuming it was designed to do so. Also, you don't want a really high launch velocity, because that would make interstellar material act like really heavy penetrating projectiles. Even a few grams impacting at over 0.5c would be unsurvivable. And though such things are rare, you'd be transiting a HUGE amount of space. So what you want to launch would be habitats designed to eventually go into orbit around some other star. They'd need fission power sufficient to make the trip, with a bit of leeway to allow them to start mining at the arrival end. And they'd need to be travelling at not too far above the local speed of debris, so that they could either dodge it, capture it, or survive the impact. (Lead shielding for impact survival, as the impact would be "supersonic" so crystal strength would be much less important than mass.)
This approach would certainly let us reach the Oort clouds, and live there as long as power held out, but I doubt that there's much fissionable mass available there, so stopping there doesn't seem viable. (Controlled fusion would, of course, change things *quite* significantly, though just how would depend on the machinery required to control it.)
Given a nearly closed ecology there are many approaches to living in space, and which is chosen is more a social choice than an engineering one. (OTOH, there are a lot of ways that just wouldn't work, without "magic technology".)