Ideally, your workouts should follow the same order every time: first, work with dumbbells, which works smaller muscles. Next, switch to barbells. Finally, move to the free-weight machines. You will have progressively engaged all the muscle groups in your body and are therefore more likely to see results in all sizes of muscles.
Standing arm curls are a great exercise for your arm muscles. To get a full range of muscle workout, flex while lifting. At the end of each repetition, straighten your arms completely by flexing your triceps. Flexing will ensure your muscles are worked through the entire range of motion.