You have gotten some good advice already. The circuit is fine for the very beginning. If you are all ectomorphs(skinning, high metabolism, hard to gain muscle) you should switch quickly to an exercise regime built around heavy compound movements. You can cover your full body into 3 workouts. Squats are mandatory. Deadlifts are good and so are barbell benches. Just learn perfect form. This trainer should be teaching you this and experiment with exercises to figure out what works for you. Just base your work outs around very heavy and proper compound movements and you will be fine. Forget isolation exercises and for the most part cardio. Do not worry about getting cut. You want muscle mass.

Weight training is huge shock to ectomorphs. Rest between workouts and a constant intake of protein is essential to build and keep muscle.

Your biggest problem though is going to be your diet if you are naturally underweight. You are going to need to eat every 2 hours of so. Protein/Carb or Protein/Fat meals spread through out the day w/ some protein and fat at night. Peanut butter and cottage cheese is good. Just eat clean food, complex carbs, protein and quality fat and you will be good. Your results will be based on your effort.