You *can* run garageband, it might just be kind of slow. Use Pacifist to install it if the iLife CD won't let you. I was able to successfully install it on my 466Mhz clamshell iBook. It needs at least 1024x768 to run properly, which the 500Mhz iBook has.
An airport card will run you at least $75 if not more. You can try a USB wireless adapter - search on eBay or try ones by Belkin and Buffalo; both of whom sometimes use a chipset that the Mac OS sees as an airport card. You can also try to get your hands a dual ethernet "snow" Airport Base Station (NOT Airport Extreme), as those have Airport cards in them. The original "graphite" Airport Base Station uses a different, albeit compatible, wireless card. You'd have to do some modding to make it fit.
Keep in mind that a 500Mhz G3 iBook will only have USB 1.1 ports, which is slow for a wireless connection.
Some other thoughts: a 500Mhz G3 will run OS X just fine, but it will be somewhat slow. I wouldn't recommend Tiger - I use Panther and I think it runs faster. Add as much RAM as you can afford - an extra 512MB will really help. For word processing, I found that Office:Mac from Microsoft ran version X much better than version 2004. Everything just loads and runs faster with Office X.
If the price is really good (like $200 or less), I would recommend you go for it. There's absolutely no reason to spend $600 on an iBook G4 or $1000 on a brand new MacBook if you're just starting out with Apple computers for the first time. Older iBooks have pretty good resale value, so when you're ready to upgrade, you won't lose much on the first one you buy.
Good luck!