You can download, at no cost, either HyperWRT firmware or the Satori firmware from Sveasoft. There are probably others available.
The Linksys WRT54GS can be configured for client mode, in which case it will connect wireless to your AP and will route to the LAN ports for wired ethernet connections to other hosts at that location. In that configuration the only wireless connection the WRT54GS makes will be to the AP, so all network connections must be via the LAN ports.
The WRT54GS can also be configured for WDS repeater mode, in which case it will connect wireless to your AP and will also connect wireless to other client mode units. In that configuration the WRT54GS will also route to its LAN ethernet ports, so both wireless and wired network connections can be used.
Note that the throughput in WDS repeater mode is about half the throughput in client mode, but in either case is almost certainly some multiple of the througput to your Internet connection. Which simply means that as long as Internet traffic, as opposed to file or process sharing between local hosts, is the only use for the wireless link, you really don't care that the througput is half for one mode as opposed to the other.
No problem. It needs only act as an AP.