A rogues’ gallery of monster-sized gas giants
nautil.us
nautil.us
If, like me, you believe that:
1. The speed of light is a hard cosmic light; and
2. The laws of thermodynamics can't be violated.
then you're left with the problem that it will take an awful long time to travel to even the nearest stars, such that it really wouldn't be a journey at all. It would be a way of life.
Anything involving reaction mass seems to be a nonstarter unless you're going to take tens of thousands of years to get anywhere so that leaves two plausible options.
The first is stellar highways. That is you use the energy from a star to propel (and slow down) interstellar vessels. This solves the reaction mass problem. This method almost requires nuclear fusion to be viable however. Many people assume it will be. I'm not saying it won't be but I'm not yet convinced it will be. The problems are massive. Why do you need fusion? Well you probably need waystations between stars and something has to power those.
The second option is... interstellar bodies. I'm talking large comets, asteroids and, of course, rogue planets. You don't need to spend inordinate amounts of energy to accelerate and decelerate them. Obviously you still have to match their velocity when they pass by but that's a lot easier to do with a much smaller object.
A large rocky object with even a modicum of ice will have all you need to house a large population for the journey of tens of thousands of years until it passes by another star.
I really think the first interstellar humans will be hitchhikers on rogue planets.
An interstellar craft orbiting a Rogue Jupiter ... doesn't have a planetary surface to land on, might benefit by available material from the giant itself (most notably hydrogen gas, a potential fuel, energy source, and component in replacing water). There might be captured moons affording other materials (mostly lighter elements presumably). There might be a slight gain in being able to gravitationally slingshot to or from the giant.
Otherwise, going it alone seems generally more advantageous.
I'm not sure that humans have the kind of longevity as a species needed for this.