Let's talk for a moment about what you wouldn't have. There would be no electrical lighting (that was a first aboard the Columbia, built in 1880). There would be no refrigeration. It wouldn't be steel-hulled (that would come with the Servia of 1881). It would likely be a steamship (though there were sail-only vessels still in use), burning coal with auxiliary sails. Rather than New York to London, you'd likely sail to Liverpool instead — that port was popular with ships heading across the Atlantic, since it cut travel time.

A five-year shipping depression began in 1873 with the Panic of 1873, so you probably wouldn't have had to pay much — as long as you had the money to spend, which many didn't.

Your ship would carry both cargo and passengers, as the passenger-only liner wasn't developed until about 1879, when William Pearce built the Arizona in his belief that a market existed for a fast, passenger-only liner. The Arizona could cross the Atlantic at 16 knots, but it burned an exorbitant amount of coal to do so. In 1875, the holder of the Blue Riband (a term we use today for the fastest crossing) was the City of Berlin, which crossed in 7 days, 18 hours and 2 minutes at an average speed of 15.21 knots. The City of Berlin was also the largest passenger ship in the world (except for the Great Eastern, of course, but that ship was all but laid up in 1875), carrying 202 first-class and 1,500 steerage passengers in a hull just shy of 490 feet long.

City of Berlin was a member of the Inman Line, which was competing with the White Star Line and several other carriers for passenger service on the Atlantic. In 1875, the White Star Line's Oceanic-class liners were brand new and making a name for themselves with their quality. These included the namesake of the class, the Atlantic, the Baltic, and the Republic. This first run of Oceanic ships was followed by the Celtic and Adriatic after the class proved successful. Larger versions of the class were built as the Britannic and Germanic in 1874 and 1876, respectively.

The Oceanic could carry 166 first-class passengers (called saloon passengers) and 1,000 steerage passengers plus a crew of 143 in a hull 420 feet long. This was a high-quality ship, with running water in most first-class cabins and electric bells to summon a steward. There was as yet no electric lighting, however. First-class was amidships, away from engine noise and with a calmer ride in violent seas. Third class was at the bow and stern of the ship, with single men in the bow and single women, married couples and families in the stern.

An 1874 account says the Republic was like a "floating palace" in first class, with a piano, library, smoking room and barber. First-class also had bathtubs and a dining saloon with chairs rather than benches.