I have budgies and a parrot, I have kept them for around six years now and wouldn't be without them.
this is my lot, from the right Sky (female) the little green one at the back is a Parrotlet (Put Parrotlet into google and you should find my forum on them .org.uk) his name is Squeak, the yellow one is Babe, on the bottom left you have Budge a disabled budgie and next to him the yellow faced one is Frank.
just so you know the green parrotlet is not kept in the same cage as the budgies he only comes out and goes into their cage when I am there.
For me THE budgies have been very easy to care for, in the time I have had them they do sometimes get under the weather and ill but I have been lucky and only lost one to illness some years ago. With the parrots I have had a lot of bad luck as they are more fragile I have lost four, one to illness, one flew head first into a wall and two died of heavy metal poisoning after chewing the window frames.
For a child I would recommend budgies I would get two so they have company as they are flock birds or even a cockatiel both of these are very easy to look after. Remember that vets bill can soon mount up and normally when you notice a bird is ill its normally in the later stages of illness and needs to go to the vet as soon as possible. In the last couple of years I have spent around £1500 - £2000 on vets bill on my Parrots I have been very unlucky but this i what you have to take on when looking after a Parrot