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Goldilocks88: Welcome to Apple Discussions! I'll do my best to offer you some advice.
1) If you're having Internet troubles, it may be due to the browser you're using. OS X 10.3 is an old operating system and not all browsers are fully compatible. You could give Camino a try and see if things improve.
http://caminobrowser.org/
2) To get a good look at which files/folders are taking up what space you can use Disk Inventory X: http://www.derlien.com/
3) Your computer can have a 1GB module installed underneath the keyboard, which would replace the 512MB module that's installed right now. The two places I recommend for purchasing memory are crucial.com and newegg.com. The 2004 iBook's RAM is PC-2100 DDR266 200-pin; PC-2700 RAM would also work.
4) You would have to buy a new operating system. You can purchase Tiger or Leopard; your computer will NOT run Snow Leopard. If you choose to go with Tiger, you'll have to check with 3rd-party retailers, such as Amazon.com. Take a look at Texas Mac Man's post here: http://discussions.apple.com/thread.jspa?messageID=9755670&#9755670. If you choose to go with Leopard, you can try calling the Apple online store to see if they still have copies in stock. If not, you'll have to check with places like Amazon.com.
Do NOT purchase gray discs--these are machine-specific and none of them will work with your iBook.
5) There isn't a whole lot of maintenance to do with the iBook; it's more important to keep adequate hard drive space free at all times. You want 15% or 10GB (whichever is larger) of the drive free at all times.
6) You can backup your data to CDs, another external hard drive or to DVDs, if a DVD burner is available to you.
7) One thing to keep in mind is that your internal hard drive could be nearing the end of its life. Hard drives tend to last 3~5 years, and yours is certainly closing in on that 5-year mark. An aging hard drive can make a machine slow down and can cause issues with software that is installed. Replacing the hard drive in an iBook is a task you can do yourself, but it can take several hours. If you're interested in replacing the drive, let me know and I'll post links to some suitable options.
I know that's a lot of information--hopefully some of it helps you! If anything is unclear, I can try to explain better.
~Lyssa
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