In an interview with GameSpot, longtime Zelda producer and director Eiji Aonuma was asked which Zelda title a newcomer to the series should start with. Aonuma considers Ocarina of Time the best to start with, as it was the first game he had worked on in the Zelda series. He then explains that the player should continue on to Majora's Mask afterwards.
Playing Majora's Mask first could be quite confusing for a first-timer to the Zelda franchise, because he or she wouldn't know the backstory behind it. This is why Ocarina of Time should be played first. Ocarina of Time is also a good introduction to the Zelda series because it is easily available on the 3DS. Physical copies may be hard to find, but it can always be downloaded via the Nintendo eShop. Otherwise, the player would have to own or buy a Nintendo 64. The game is also available on the GameCube, not to mention the Wii and Wii U via Wii virtual console.