I hear noble macaws make excellent pets but can be hard to come by. Yellow collared and illigers may be two other good options, but they are not quite as common as some other species. Red fronted macaws do make wonderful pets, too!
I'm not really a fan of recommending a large parrot species to an owner that has limited experience handling and caring for various sized species. It can work, if you do the research and you and your family are prepared for that jump in size, but it can also go very wrong. You need to learn the pros and cons of owning a larger parrot. They require a minimum of a 40" x 30" cage, if not larger, it will be more expensive to feed them and provide toys for them, it may be more difficult to handle them (when they bite, it can cause a lot more damage than a budgie can!), they are noisier (this could be a problem if you live close to neighbors), etc.
Keep on researching the various species! Maybe you'll come across one you never thought of before! Interact with various species to find one that will fit into your family! Some species may require a special diet (macaws may need a higher fat diet than other species, amazons may require a higher vitamin A diet, african greys may require higher vitamin A and calcium diets, eclectus may require a fresh food based diet [i.e. no seeds/pellets or in minute amounts], lorikeets require a nectar based diet, etc), so do learn what the birds require before purchasing one!
You may want to look for some local rescues who could allow you to interact with their adult birds so you can see what they may be as adults (of course, this will vary on how they are raised). You'll also want to hear just how loud these birds can be before getting a young parrot (if that is your decision to do so). Make sure you can handle the noise before it's in your home!
