Ten years ago, Maicoll Gomez and his family immigrated to the United States from Cali, Colombia. Their first apartment was a one-bedroom in Union City, N.J.

“My parents instilled in us the values of working hard to achieve whatever we want,” said Mr. Gomez, the middle of the three siblings, all in their early 20s. “You hear in Colombia that the U.S. is the greatest country on earth. We moved here without speaking English and without having the right clothing for winter, which, honestly, sucked.”

The Gomezes moved often, renting two- or three-bedroom apartments “depending on how many of us were living at home,” Mr. Gomez said. “Each of us went off to college in different years.” Their most recent rental was a two-bedroom in Bayonne.

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In the summer, they sometimes woke up early to catch the 4:40 a.m. bus to the 16th Street Pool in Bayonne. Swimming was a family passion, and all three earned swimming scholarships to college.

The oldest, Jonathan Gomez, competed for Colombia in the 2016 Summer Olympics in Rio and is currently training for the 2020 Summer Games in Tokyo. The youngest, Valentina Gomez, who is headed to business school, is a competitive swimmer as well.

As they grew, the three siblings began to translate for their parents. Maicoll, who works in real estate investment, also did his parents’ taxes and helped them buy a car. He decided that owning real estate was an important step toward a stable and secure future. And the monthly payments to rent or buy were not that different.

“In order for us to keep moving forward with the American dream, we needed to acquire a home in an area that I projected to increase in value over a short period of time,” Mr. Gomez said. “We know most people live in apartment complexes, but you never really own it, and you have to pay all these fees.”

The Gomezes planned to remain in the same general area, in a place convenient to stores and public transportation, preferably with a driveway. And the backyard had to be big. “I wanted a pool, a dog and a trampoline,” Mr. Gomez said.

Working on behalf of the family, he considered a range of types and sizes, including fixer-uppers and flips, single-families and multifamilies, where rental income would help with the mortgage. Most were built around 1920. The family’s budget was up to $500,000.

Among their choices: