Training individual muscles when first starting out is something that is commonly done, and completely unnecessary. Look into full body programs that you are capable of doing, even if they require you learning a new exercise. Since you're new to this, I suppose they're all "new" exercises.
A very popular beginner program is Starting Strength, aka SS. Its very simple, effective and will open the door for you to go in just about any direction. Its full body, and well balanced. Though it doesn't have isolated arm exercises, your arms are being effectively worked, and are worked with more load than you can handle with a dumbbell.
The Workouts Recommended for Strength Training | Starting strength training
I'd recommend following them in the order the 1st link has them in. After your first couple workouts, an explanation as to their order will become unnecessary. I promise.