At today's technological level star travel in a reasonable time span is impossible. Our fastest rockets travel 30,000 miles per hour. At that speed a 19 light year journey would take 433,790 Earth years.
For star travel to be feasible, space technology would have to be at nearly light-speed. Therefore, our stories should be at least a century from now. Technology snowballs. We can safely postulate terra-forming techniques, likely developed to save the Earth from pollution death, by that time. If successful, Venus and Titan could be terra-formed.
With three terra-formed planets, numerous space stations and ore bearing planetoids, what would be the human motivation for star travel. Much too expensive just to satisfy curiosity, and would certainly not be due to population pressures. There are cheaper ways to reduce population, among them, war, euthanasia, and enforced sterilization.
No human society can make all its members happy. There will always be dissident groups who believe they know a better way to live. Religious and political rebels would want their own Eden or Utopia. There would also be "lone wolves" wanting to live minus governmental interference. But who would foot the bill to find worlds for these people to emigrate to? Not any government.
A society hamstrung by anti-death-penalty laws, might want a terra-formed planet as an interstellar Botany Bay. There-by removing dangerous types from Terra. However, are those who object to the death penalty likely to finance the first chancy voyages? Unlikely.
One non-governmental group with the financial clout to do the job is private enterprise. Even today NASA is consulting with private enterprise to take over the space program. But private enterprise's overriding motivation is profit. It wouldn't be enough to insure sole exploitation rights to planets discovered. There might not be any planets, nor anything small and valuable enough to be worth the return trip.
I think Warren Salomon's article "The Economics of Interstellar Commerce" (Analog May 1989) gave the best answer to this question. He postulates compound interest as the motivation for star travel.
Salomon contends that one can use Terran banks to make huge profits by investing in an exploration company, putting one's remaining funds into an interest bearing account, then climbing aboard the space ship.
Returning three ship-years later, twenty-four Terran years have passed with the resultant accrued interest. One's original investment having multiplied five or ten times, "depending on interest rates".
There are risks Salomon didn't go into. What if during the 24 Terran years the investment source has been nationalized? How are you to prevent the government, or your heirs, having you declared dead after seven years? Protective laws would have to be passed, and entrenched watchdog groups set up to protect the investor's interests before any one could be induced to part with the necessary backing.
Another major problem is ship personnel. A several scientists, and both genders, would be required to operate the ship. But any scientist that goes on this journey into the unknown will return to find themselves badly outdated by normal technological progression.
What over-riding motivation could send a highly trained individual out into space at such a cost? Probably not financial reward. It's true that these explorers would potentially reap new information about the nearer stars. But how many would be willing to be that specialized?
The vast majority of any group are conservative, including inherently nosy scientists. Only a small number climb mountains "because they are there". Plus, they must be able to live compatibly in close proximity with a wild mixture of personalities. In time, it's reasonable to expect these exploration teams to develop into a subculture who never leave space - interstellar gypsies. With an inhabitable, or terra-formable planet at the journey's mid-loop, the story teller can branch out into all the secondary motivations. With our original investors and ship's crew guaranteed sole exploitation rights, more financial reward would be realized in selling whole planets to Solar societies' malcontents. Even an interstellar Botany Bay wouldn't be impossible.
Like our original investors, some people would purchase round trip tickets. In effect time traveling to still be alive when cures for terminal diseases might be discovered, or bank accounts vastly increased. Statute of Limitation Laws would have to be changed to protect society from criminals who slip away on space ships to return long after the limitation lapse without actual risk to their liberty during that time.
Sooner or later, it's logical to suppose that a scout ship would locate a planet with intelligent life. This would cause mixed reactions on Terra. Many scientists would consider such an event a reason to celebrate. Cooler heads might have trouble preventing the more enthusiastic types, from immediately inviting these interstellar cousins to the party.
What about the original investor? Companies and tycoons aren't noted for accepting loss gracefully, nor are aggressive, ethnocentric malcontents. Conquistador types would attempt to enslave, or eradicate the native populations. If an aggressive faction made the return trip, the Carl Sagan and James Burke types could follow to prevent genocide. The intended victims might also deliver formidable surprises. In conflict, is story.