You should do 30 - 60 mins of exercise focusing on your muscles on the days you do your strength training. You should 40 - 60 mins of cardio on the days you do cardio, for fat burning.
A 15 min walk is a good warm up, but won't give you a significant calorie burn if you have fat to lose. 15 mins of working out with weights doesn't really give you much time to challenge your body (and you have to challenge it to change it).
Look up workouts on youtube (there are tons). You can search on 45 min cardio or 45 min toning or strength training. See the different things available, and go for it.
Workout with weights one day, do cardio the next day. Your cardio workouts can include body weight exercises for extra muscle toning. On days 5 and 6 (when not using your dad's equipment) maybe go for a long walk or run. Give yourself at least 1 rest day a week. If you want good results, shoot for working out at least 5 days a week, or 6. Once you hit your goal, you can drop to 3 - 4 days a week for maintenance.