I have done both trips in November/December. March is coming out of the rainy season, but could still be wet in the Andes. One thing to consider, is whether or not you will be trekking to Machu Picchu. If this is the case then you really need to spend at least three days in Cusco to acclimatize due to the mountain passes you will be hiking over. I hiked the Salkantay trail, which went over a 15,000 foot pass. I only saw glimpses of 20,000 foot Salkantay because of the rain. It was quite cold.
You can always take the train from Cusco to Agua Caliente and take the bus up to Machu Picchu. This means you will not need to acclimatize. I would recommend taking the vista dome luxury train ride back. It's quite fun. Cusco is a destination in itself. I would strongly recommend getting a guide and touring around the area for a few days. Chinchineros, Pisaq, Moray, Maras Salerinas are interesting. I also suggest taking a docent tour at the Larco Museum in Lima. It is excellent, having artifacts from not just the Incas, but the other civilizations that preceded it.
The Galapagos are always good weather. are you considering taking a cruise? These are very expensive but also very worth it. They work better if you are traveling as a single.
One destination I must mention is a 5 day trip to the Tambopata research station. This is in the Amazon basin on the east side of the Peruvian Andes. It is AMAZING. This is a Macaw research center. I have never seen so many and different macaws in my life, as well as hundreds of other animals. You sleep in a thatched lodge and go out at least 3x a day with naturalists.