Welcome to the wonderful world of the Apple iBook G4
I wont say they don't have their problems. The most common relates to logic board failures. One of the things you have to establish is the fact these are 8 or more years old. Your not going to get the same performance from an 8 year old iBook as you would with a modern MacBook Pro.
If your running Mac OS X 10.5.8 (Which your tags says) Then you should be using iTunes version 10.6.3
You can do most thing with this version of iTunes, including downloads from the iTunes store, rent or buy films or buy music. If your iPhone has iOS 6 update, then you may find that with the iPhone 4S and iPhone 5 it wont sync with this version of iTunes. As that does required iTunes version 10.7 which is currently only available for Mac OS X 10.6.8 and above. You can't install Mac OS X 10.6, 10.7 or even 10.8 All of these versions of Mac OS X require an Intel based Mac
Your currently on the latest version available for an iBook G4 above 800Mhz. (This is Mac OS X 10.5)
You will find some thing are not very good. Like some Flash web sites such as YouTube.
This is due to the flash player having not been updated for Mac OS X 10.5.8(out of date)
There are alternatives to YouTube on the web, Like YouView application which will run YouTube videos from your desktop. You can also install a web browser called Camino which handles the web better than Safari for Mac OS X 10.5.8
Other than web site restrains like YouTube or FaceBook Flash Games, Your iBook should be fine to do almost anything you require. It wont run any newer Mac Applications, you will need to be mindful when buying or downloading sofware to which it will or will not install.
I'm currently using a PowerBook G4, which runs some useful old application with ease.
I've no retrains on it use and I'm very happy to use it as my daily computer.
All comes down to what you want to use the iBook for.
Hope this helps