Q: Need to do an installation that involves four devices: an ADSL modem, a Linksys wireless router, the Airport Extreme station WITH its respective reception base. How do I accomplish this, in order to have internet routed to the Apple small receiver end?

To potentially satisfy your client's goals, the 802.11n AirPort Extreme Base Station (AEBSn) would need to be connected to the Linksys router by Ethernet, and then, the 802.11n AirPort Express Base Station (AXn) and the AEBSn can be configured for an extended network. Note: For this configuration to work, the AEBSn would also need to be reconfigured as a bridge (Connection Sharing = Off (Bridge Mode))

I am not sure why we need the linksys in this equation at all?

Modem (bridge + pppoe) -->-cable->- Router ->-cable-> AEBSn (WAN or LAN?) ----wireless----> AXn

Actually, when in bridge mode, all of the Ethernet ports on the AEBSn are just that, Ethernet port. It really doesn't matter which port (WAN or LAN) you connect the Linksys to. However, I would recommend the WAN port for consistency.

Modes:

Modem - BRIDGE + PPPOE

Router - DHCP

AEBSn - BRIDGE

AXn - (left alone by itself)

The AXn would be configured to extend the AEBSn using the link I provided earlier.

Funny enough, Linksys devices are told to support a wireless range link of 500 meters; and it's not working with the router alone.

A 500 meter range for a consumer router, even in free space, would be highly unlikely. I would expect you would be lucky to get a useable signal at 100 meters. By "useable" I mean a signal that can support a bandwidth of 54 Mbps or better.

It's important to understand that although the Express will "boost" the signal level, it will only repeat that signal with the bandwidth that it receives it. Typically you will want to place the extending AirPort within a 25+dB SNR (Signal-to-Noise Ratio) range of the station that it is extending. SNR does decrease with range and will depend on a number of factors that are introducing signal noise into the environment. Based on experience, I would say the average distance the extending base station would be is within 15-30 meters of the extended station to still provide a useable signal.

Do you recommend that the client purchases a long range antenna to fetch the link, from the receiving end; and use only the Linksys Router?

For these types of distances, you may want to consider a point-to-point type solution. You can find a number of them here.