For strength training, dumbbells offer a ton of versatility and produce real results. I tend to prefer dumbbells over barbells for myself and many of my clients. Dumbbells allow you to exercise each limb independently, which is difficult (but not impossible)to do with a barbell. Dumbbells are much more
than any machine could ever be and allow you to train in a variety of positions and movement planes.
You can lift two dumbbells at once, one at a time, or even in an alternating pattern.
I believe that when training with one limb at a time you will develop greater balance, core strength, limb strength, coordination and will stand a better chance of fixing any weaknesses you may have.
Dumbbells come in a variety of shapes and sizes. I recommend using they heaviest ones you can handle, with proper form, for a given exercise.
In addition to the traditional curls and flyes, I recommend trying many of your overhead presses, deadlifts and squats with them. Dummbbells also allow for "Compound" lifts like a lunge and a press, or a lunge and a reach, a squat with a press and/or a curl.
Beyond the slower strength lifts, you can easily perform cleans, jerks and snatches with a dumbbell. If you do not have a kettlebell then grab a dumbbell and try some
Dumbbell Squat and Press