Marmoset monkeys are a wild animal. They are not meant to be someone's sweet little pet. No matter how much training one has, no matter how young the marmoset is when you acquire one, he or she will still be essentially an animal that not belongs to the wild, but wants to be there. They have natural instincts that you can't ever "tame" out of them. For this reason, they do not make good pets.
If you are set on getting a marmoset to turn into the household pet, you should be prepared to give him or her everything that you are able to to meet his or her needs. The monkey will need time, attention, financial support, and training at the very least. Imagine that you are having an infant, but one that is never going to grow up and become self-sufficient. For the lifetime of the monkey, you are going to be the one that is responsible for meeting his or her needs entirely.
Marmosets have personalities and though they are not typically mean animals, they do throw fits and have temper tantrums. These have been known to result in serious injury as the marmoset will slap, pull hair, or scratch to get its way and your attention. They do not like being left alone for long at all and if they are unsupervised for too long, you will end up with a destructive and ill-mannered pet. The marmoset may even take up the habit of biting, which is not pleasant and is not healthy in the least. The marmoset will need almost constant mental stimulation, so if you can't be with them at least ninety percent of their waking hours, this is not the pet for you!
When marmosets, or any other monkey, hits the age of sexual maturation, there can be big problems. They will have instincts and urges that are very strong. This is much like human teenagers, but they won't have the capacity to really understand the etiquette rules necessary for societal acceptance. This can cause some very embarrassing moments for both you and other people.
In general, unless you have extreme training and experience with animals, monkeys in particular, marmosets do not make good pets. This is not their place in the world. It is unfair to the marmoset and often, does not lead to a pleasant experience for either of you in the long run.