Painting a house is a serious undertaking––it looks simple but involves a lot of preparation and hard work. An undertaking is a job or a task you commit to. The word also can mean the profession of funeral management.
When you take something under consideration, it means you're not necessarily going to do it, you're just going to think about it. When you take something on, you've undertaken to actually do it. The word undertaking suggests something that involves quite a bit of work. Organizing an Oxfam hunger-day at your school is a significant undertaking, but it's worth all the effort.