Molly Quinn and Ben Sheen were classical musicians in New York City who had known each other professionally for years before they started dating in 2019.

Ms. Quinn, 48, a classical singer and singing teacher from Chapel Hill, N.C., performed at places like Carnegie Hall and the Brooklyn Academy of Music. Mr. Sheen, 36, an organist and conductor from London, received a masters from Juilliard, and then stayed in tow afterward for a job at St. Thomas Church Fifth Avenue.

But the beginning of their relationship was also the beginning of a difficult period: Ms. Quinn’s father died after a stroke not long after they got together, and her mother died from cancer a few years later. Mr. Sheen moved back to Britain for work in January 2020, right before the Covid pandemic restricted how often they could see each other. By the time they married, on New Year’s Day in 2022, they had already been through a lot together.

They eventually moved to Cambridge, England, where in 2023 Mr. Sheen began working as the director of music at Jesus College at the University of Cambridge. Ms. Quinn continued working as a freelance classical singer, mostly in the United States but soon in London, too, and gave private singing lessons in Cambridge and taught university students.

Once they were finally settled, they were eager to launch into their new life, and wanted to quickly buy a property. But Mr. Sheen’s job provided housing in Cambridge, so they decided to purchase a vacation home that would serve as an escape from city life.

“We realized we really wanted a place that was ours, to kind of get away from the hustle and bustle of Cambridge,” Ms. Quinn said.

Beautiful views and access to walking trails were a must, but they didn’t want to be too far from the city since they’d be driving back and forth. They also wanted to be able to easily rent out the property when they were in Cambridge or traveling for work.

The couple had spent time vacationing in the Peak District, a hilly, green region that includes hundreds of miles of countryside in the heart of England. They loved going on scenic walks and exploring nature spots, local landmarks and picturesque villages. So it seemed like the perfect place to look for a second home.

They wanted two or three bedrooms. Mr. Sheen said they also “didn’t want to do a huge amount of renovation,” but were also looking for modern amenities like double-glazed windows to protect from the blustery winter weather, as well as rustic touches like a wood-burning stove for “that cozy cottage feeling.” Private parking was also important since the Peak District attracts a lot of tourists.

Their budget was 275,000 to 375,000 pounds, or about $368,000 to $502,000. They decided to put down about 170,000 pounds ($227,000) in cash and then take out a smaller mortgage.

Liz Agar, an associate director at Saxton Mee, the real estate agency they used, said that when the couple was looking in the second half of last year that it was “probably a little bit more of a buyer’s market than it’s been.” More properties were available and there was less competition than during the pandemic frenzy of buying in the countryside.

“We looked at a huge variety of places,” Mr. Sheen said. “That was the sort of fun of it, not to have one thing in mind.”

But three stood out:

This two-bedroom, 641-square-foot cottage in the bustling village of Ashford had a stone fireplace, a wood-burning stove and an open-plan dining area. Ms. Quinn appreciated the kitchen, which had built-in appliances. There was loft storage and a private rear terrace and garden with a shed.

They were told it was a bargain in a town where it can be very expensive to buy — “a quaint little sort of Cotswold-esque” village, Mr. Sheen said. But the property didn’t have parking, which could be a problem in a tourist destination, and there were cracks in the ceiling. The asking price was £295,000 ($394,000).

This ground-floor apartment with about 915 square feet was centrally located right on the River Wye in Bakewell, a scenic market town popular with tourists and retirees. It had a private, leafy terrace that overlooked the river.

“You could picture on a beautiful summer’s day it was just idyllic,” Mr. Sheen said.

The town’s popularity meant that they would have no problem renting out the property, he added. It had two double bedrooms with built-in storage, and another room that could be a third bedroom or office. It had an open-plan living room and a parking space, though the kitchen needed updating. The list price was £365,000 ($489,000).

This two-bedroom terraced cottage had 608 square feet and was outside Litton, a small, quiet village. The house was next door to a farm, so it had cows roaming by and seemed “so peaceful,” Ms. Quinn said. It had well-preserved wood paneling and a stone fireplace alongside modern fixtures after a major refurbishment in 2018. A summer house and a patio overlooked the rolling hills of the countryside.

The bedrooms were on the smaller side, and it was more remote than other properties they viewed, but it did have its own parking spot. They were also warned that “you have to keep an eye on your roof because it does get blown sideways” in winter, Mr. Sheen said. The asking price was £325,000 (434,000).