Using a USB Wi-Fi adapter is possible, but you will notice that only a few modern devices (with WPA2 security) support Mac OS X 10.4. USB adapters depend on special software, so make absolutely sure that the supplier can provide you with the required driver software (or at least a valid download link). Mentioning a certain adapter model here could be misleading, since a hardware revision may or may not work with previously available software (but Edimax EW-7811Un at least appears to have had drivers for 10.4). A USB 1.1 port will limit the speed (to less than 12 Mbps).
A wireless Ethernet bridge on the other hand does not (normally) need special driver software, and can thus be used under almost any operating system. WPA2 security is standard on modern devices. You will find a nmber of wireless Ethernet bridge models that should be suitable in this case. You may want to have a look at, for example, Linksys WET610N and Netgear WNCE2001. Even some Wi-Fi range extenders with an Ethernet port (such as TP-LInk RE200) have wireless bridge capabilities.