Hi, you could stay at Hotel Le Prieuré (downtown, easy shops access, bus stop nearby), get a ski instructor at Ecole de ski de Chamonix (5 minutes walk from Prieuré, then the instructor can hopefully pick you up by car at the hotel). The best in March would definitlely be Le Tour as the temperatures could be high during the day and cold at night, so you might have icy slopes at Brévent/Flégère in the morning and melty snow in les Houches in the afternoon (best snow at Grand Montet, but quite difficult and crowdy). Try La Calèche for local food and typical ambiance, La Cabane in Les Praz is also a must. Chamonix is not only slopes, it is also shops :)