Both are mainstream. Quark is slightly more popular with people whose roots go back to when Quark was the professional's choice. Either is mainstream, with Adobe offering a more complete family of applications and a more comprehensive workflow model. If I were buying for the first time today I'd probably go with InDesign - but that's just me. Five years ago I would have picked Quark.
How long it would take to get proficient is a tough question. Depending on what your goals are, and how much typographic, print production, and design background you have, you could be talking weeks or years.
What are you looking to accomplish short and long term?