Cara,
I suggest it depends on your characters. I'm fond of Jane Austen's works and I'm a middlebrow. But Jane was early 19th century and probably not popular fiction in 1912. If your character likes the classics, she may prefer to read Austen or the Brontes or Dickens or Trollope or Thackeray, even though they weren't modern - and some aren't all that light. Oscar Wilde's "The Picture of Dorian Gray" Mary Shelley's "Frankenstein" (old classic, but was probably popular then) Did Teddy Roosevelt write a book?
A. Conan Doyle's Sherlock Holmes stories would be a good bet for a boy or even a man. (He was writing them off and on until 1927) And Doyle wrote other genre fiction too. Same with Kipling. Mark Twain (Samuel Clemens) died in 1910, but his major works are always popular. Booth Tarkington. Lucille Maud Montgomery (her Anne of Green Gables and others of the same genre) I don't know if H.G. Wells was writing then. Hemingway wasn't yet, but a bio about him might say who influenced his early writing.
Are you close to a large library (public or university)? If so, there may be copies of old magazines like the Strand or Colliers or Liberty. They may be on the internet as well. Several good and not so good writers wrote short stories for the magazines. Or try the newspapers on microfilm. Sometimes papers (like the New York Times) reviewed the new books.
Sax Rohmer and Jacques Futrelle for mysteries (and Mr. F. died on Titanic. So did W. T. Stead) Elinor Glyn may be been writing then. P.G. Wodehouse had not started his Jeeves or his Emsworth novels yet, but he was writing public school stories for boys in the early 1900's. I don't know offhand, but I think Psmith and Stanley Featherstone Ukridge may have been among his characters way back then.
I believe Walter Lord mentioned Owen Wister's - "The Virginian" was in the library on board in his "A Night to Remember".
And then, not everyone liked to read for pleasure. I don't know if Marconi provided a news service from Cape Race, but there was a shipboard newspaper, wasn't there? There may be editions of the Times (London) and other papers on board (dated the day of sailing). Businessmen would want to know what was going on.
