If you are trying to build a home gym on a limited budget, you may have to make a choice whether to purchase a dumbbell set vs. barbells for the start of your gym. I will go over the advantages of a barbell set in this article. You can refer to my article The Advantages of Using Dumbbells over Barbells for Your Workout Routine for the reasons why you would want to use dumbbells over barbells.
With barbells the most obvious advantage over dumbbells is the ability to do heavier weights. If you do a 200 pound Bench Press, it'll be quite unlikely that you can do a Dumbbell Bench Press with two 100 pound dumbbells.
That leads to the next advantage which is you are much more likely to get access to heavy weights through the use of a barbell. If you were to join a gym, many gyms do not have 100 pound or more dumbbells. If you are creating a home gym and need heavy weight, buying a barbell set and the individual weights can be cheaper than buying individual dumbbells. The only exception to this would be an adjustable dumbbell set, depending on which one you get.
If you are using barbells, you are less likely to need human spotters. If you will be working out by yourself in your home gym, you can buy metal spotters for your bench press set or squat rack. Using the example above for the Dumbbell Bench Press with 100 pound dumbbells, if you were to go to failure and did not have a person to spot you, you could risk tearing your forearm or bicep muscles while you dropped the weights or damage your floor. Having metal spotters on each side of your barbell Bench Press allows you to drop the weight, have the metal spotters catch the bar and slide underneath it.
You simply cannot do most power exercises without a barbell. For instance, the Clean and Press or Deadlift would never have the same effect using dumbbells over barbells even if you could find the right amount of weight for them. Part of their effect is to build overall musclarity by getting the whole body involved in the movement and holding two indivdual dumbbells in your hands really limit that effect.
A barbell makes it harder to cheat while performing an exercise. For example, doing Dumbbell Bicep Curls may cause you to sway side to side without you even realizing it. Barbell Bicep Curls will limit your ability to sway to help you lift the weight. You may just be arching your back to lift the weight which is an easier problem to notice and can be fixed by concentrating on standing straight or leaning against the wall.
A barbell set will be most appropriate for someone who is trying to build a lot of power and muscle by themselves in their home gym.
More of my workout advice:
Are Bowflex SelectTech Adjustable Dumbbells suitable for you?
Should you buy Bowflex SelectTech Dumbbells in a store or online?
Why you would want to use dumbbells for your workouts
How I lost over 40 pounds in 6 months with some simple diet changes
Upper body exercises with no equipment needed
Lower body exercises with no equipment needed
Cardio exercises with no equipment needed
The Different Ways of Doing Dumbbell Bicep Curls
Inflatable Exercise Ball Exercises for Men