Diet is more important than exercise for losing weight. Unless you take it very seriously (30 mins of high intensity a day or 50 of moderate and up) or are very overweight, you will most likely maintain weight through exercise, though your fat % will drop. And cardio > lifting for losing weight.
The first 20-30 minutes of exercise are by far the most important if you are doing only cardio or only lifting (http://well.blogs.nytimes.com/2012/05/04/the-surprising-shortcut-to-better-health/, http://well.blogs.nytimes.com/2013/04/23/ask-well-double-the-workout-double-the-benefits/ ). You can do both and some research suggests this is more efficient in a long workout (http://well.blogs.nytimes.com/2012/05/02/mixing-weight-training-and-aerobics/).
HIIT is the most efficient form of exercise for cardio but it can be unpleasant. Some find it easier as part of a class. For lifting, there's practically no good research (so go w/ whatever plan you find) but as beginning lifters you can both become much stronger with comparably little effort.