Fusion Starship

The achievement of fusion sufficient to generate more energy than it takes to make it work will solve more than our energy problems here on Earth.

If we can build a portable fusion engine to drive a starship, its exhaust velocity would likely be about 6 -7% of the speed of light. Spaceships can be engineered to go about twice as fast as their exhaust velocity. So the possible speed of a fusion starship can be 12.5% of the speed of light, and maybe a little more.

The distance to the nearest star is 4.25 lightyears. We could get there in less than 40 years (accelerate 2 years, cruise 33 years, decelerate 2 years), study it for a year while we refuel, and either choose a landing site or go on further to Centauri A or B to search again.

We don't have to find an earth-like world. We want a large Mars-like world, a lot of asteroids, water and nitrogen, and a small gas giant. If we find those around a small G class or large K class star, then we have a new long term home for humanity.

This starship can reach the next star system within a human lifetime. But 37 years is still a very long time and, unless you plan to live for centuries, no one is coming back. This is a colony ship, not an exploration vessel. Yes, you can send a probe first, but don't forget about talking to it now and then, to keep it functioning. Still, any people who go will want to have families and colonize a new star system. They are pioneers, not just bold adventurers.

Where should they look?
A smaller G class star would last longer, with less UV, than the larger one where we are now, and a larger K class star would live even longer and still have a suitable spectrum of visible light (unless our insects need more UV to see by.)

Jackpot would be finding a G4-G6 star, with one or two new places to live, plenty of accessible resources, and lots of fuel. Ideally, just inside the outer edge of the habitable zone:

*Look for a a barren, cool planet, or maybe two. We don't want to disrupt a thriving ecosystem. We could learn from a new set of microbiology.
*Preferably one with 75 - 90% of the mass of Earth, since Earth is just a little bit too heavy for single-stage-to-orbit crafts.
*The right composition: Nitrogen & CO2 atmosphere, lots of water as ice or liquid, abundant "metals" for industry, and an internally generated magnetosphere.
*And ideally, a small round moon, to stir up the magnetosphere and provide a staging area for space infrastructure development.

In the nearby icy zone
*An accessible orbit full of planetoids, from a broken or aborted planet, with all of the carbon, ices and metals needed to support life and advanced technology.

And just beyond those:
*One or two small-to-medium size hydrogen-helium gas giants with plenty of useful isotopes readily accessible for fuels.
 *A few round moons made of water ice, and liquid nitrogen and methane. We will need these for building new rotating space habitats, and for any terraforming we may want to do.

The methane comes in handy for chemical fuel, to launch from a planet's surface, if we don't build a better way.

We will probably use a closed cycle "nuclear lightbulb" for interplanetary transport, with plutonium to heat plain hydrogen as a more efficient fuel. It uses a clear crystal barrier between the plutonium and the hydrogen to prevent radioactive contamination. That can create  a specific impulse about 5 times greater than the chemical rocket that got us to the Moon. We could actually do this today, but we fear an accidental meltdown.

Of course, this set-up closely resembles the situation we find ourselves in here, optimized for a technological civilization.
Isn't it interesting how it looks like our system has already been optimized to both challenge and reward us for trying to reach space?

If you find these, you are home.
Good Luck.