What they want is to have one SSID and be able to move about the building and not even have to think about connecting to a different SSID. We want it to just automatically switch over to the stronger of the APs.
I did this some time back with two APs, both flashed with DD-WRT firmware. IIRC, one was configured as a standard AP and the other one was configured as a wireless client bridge/repeater. They both had the same SSID, and security key, and my transition between APs was seamless. I didn't have an existing wired network in place like you do, but I imagine that won't present a major issue for you.
If all you need is 2 AP’s, then you can just go with any wireless N AP’s you can find at Office Depot or Best Buy, link Linksys or D-Link. The easiest way would be to have 2 separate AP’s (one in each wing or side of the building) with each having there own SSID (Wireless_East and Wireless_West).
That would be the easiest and cheapest to setup