I think a bird is an excellent way for you to learn responsibility, compassion and have a fun pet (if you already like birds). My biggest consideration (assuming you are in middle or high school) with a parrot is when you go to college, they may not accept pets in the dorms nor do many "starter" type apartments. Unless you plan on staying at home, your mom needs to also be on board to care for this bird for a few years when your older until you can resume its care in a stable home. Keep in mind, medium parrots live 20-30 years, large parrots 60+. Many young people are perfectly capable and willing to care for a bird while at home, but too often the process of growing up leads to the bird being rehomed. So long as this has been discussed and agreed upon with your mom, I think time wise you are able to give a bird a reasonable amount of attention.
As for species, a medium sized bird (conures, caiques, Indian ringnecks, Quakers ect...) would be the logical "next step" up after budgies. Full size cockatoos are among the most difficult birds to keep, and only very experienced parrot owners really have the skills required to care for a too. If you really like full size cockatoos, then perhaps a cockatiel would be a good choice for you at this point in your life. They are still very neat little birds, are still a bit larger than budgies, but don't quite require the level of experience their larger relatives do. Owning a goffin can be a long term goal for you, once you are older, stable and completely ready for that level of responsibility (large parrots are like having a baby in their care, expense and time needs).