To build a one story or two story house is a fundamental home design decision. Luckily, the pros and cons of "building out" versus "building up" are clear cut. The best house design depends on your individual situation.
One story houses are easy to build. If you're planning to build your own house, this is an important consideration. You'll soon learn that it's much, much harder to sheath walls, build the roof, and complete trim work on a two story house. Scaffolding is a pain to erect and everything takes about 5 times as long to do when you're working up high.
One story home designs can also be more accessible for older or handicapped people. A staircase is a real barrier to some people, and we'll all get old one day.
Two story houses have a smaller footprint so they can fit on a smaller parcel of land. Land is expensive, particularly if you're building in a city.
A two story design also has a much smaller roof and foundation than a one story house with the same square footage. This can save money on concrete, trusses, shingles, etc.
Unfortunately, a two story house needs a staircase, which is a big space waster in a small house. This is less of a problem in a big house.
Last, but not least, a two-story design gives you the opportunity to build a porch on the second floor. To me, that's a very desireable design feature and was a major part of my decision to build a two story home.