What are three exercises you would recommend if I wanted to work my shoulders and back in the same gym sessions?

I personally love the good old Bench Press exercise as this targets several of the muscles in the upper body at the same time. I would also recommend the Upright Barbell Rows which give the muscles in the chest, shoulders, upper back and arms a good workout.
The third exercise that I would recommend would be the Overhead Barbell Press which works several of the upper muscle groups at the same time. All these exercises will let you handle much more weight and therefore build strength and muscle.
Always give yourself the goal of adding 2 to 5 pounds to the bar for every exercise you do when working out. This will help stimulate your body into growing extra muscle which will increase your overall strength.
Adding compound exercises to your workout routine is the best way to build strength throughout the muscles in your upper body. This additional strength will make it much easier for you to add more weight to the bar at each workout.
Since your muscles are finding it easier to compliment each other when lifting and lowering weights you are able to keep the correct form through the exercise. Keeping the correct form is important and will cut down the chance of injury.

Read more here about the science behind gaining muscle quickly