Unfortunately you assume wrong! The G3 Lombard (both 333 and 400Mhz versions) have no internal airport slot, therefore cannot use the airport card from your ibook.
They do however have a PC Card type I/II slot which you may be able to use with a wireless card of some form.
With regards to browsers, I've never had OSX on my G3 Lombard 333, keeping it as one of the few machines I have left that can boot natively into OS9. I do run 10.4 on my G4 laptops and I use Camino 2.1.2, Safari 3.2.1 and Firefox 3.5.19. I find Safari has java issues with some sites where Camino is more successful, but I find Camino to be generally slower than Safari. Firefox I don't use that much as I generally use either Safari or Camino - neither of which are ideal to be honest.