Steen, please read Michael's:
Taming Article
Caging article
Bad Rewarding article
Good Behavior article
Potty Training article
Then read the rest of Michael's blog. Also check out Barbara Heidenreich's website. She explains training terminology (very important to know and understand!) and has some other helpful stuff. Some people don't like BirdTricks, but their blog has lots of helpful articles too. Read a lot about what it takes to have a tame, trained, and well-behaved parrot. Also read about parrot-proofing your house, which you will need to do whether it is out of the cage most of the time or not. You will either be fascinated by parrots and want to learn more, or you will decide that owning a parrot is not right for you.
If you decide that a larger parrot is really what you want, put lots of work into the budgie you have now. Train him, play with him a lot, and try the things in articles. Then go to a pet store, breeder, shelter, or rescue and handle as many different types of birds as you can. A pretty macaw may sound good until you see the beak up close. Some rescues can also match you to a species that you will best be able to handle and connect with. Then, research that species as much as you can. Research temperament, common issues, and the dietary needs of that species. Calculate how much it will cost for you to care for that species every year, including toys, cage accessories and vet check ups. If everyone did this, there would be way fewer abandoned birds!
As far as cockatiels and budgies being compatible: it's never a guarantee. Each bird has its own personality. Even if you get a cockatiel and it gets along with your budgie, they shouldn't share a cage. Some people have both and they are best friends. Others have both and the budgie bullies the cockatiel or vice versa. Proper socialization is very important!







