It's entirely your choice at the end of the day. Both Monk and White Mage are in demand for the end game (by which I mean Extreme Primals and Second Coil), so you have to ask yourself what job do you feel you are best at and, more importantly, which job is the most fun?

What I do suggest is once you make your decision, throw all your available resources (by which I mean Zodiac Weapon, Soldiery, Syrcus Tower gear and of course the unidentified allagan tomestone you picked up) on your chosen job. The reason being is that if you split between both jobs you'll end up being more of a bits-and-pieces player, and some of the harder content usually calls for job specialisation as opposed to generalisation.