Connecting two Linksys wrt54GL routers

Greetings. Here's my layout...

Setting up free wireless internet using two WRT54GL routers flashed with
DD-WRT v23 (std). A single dedicated computer will be the DHCP server
(running publicIP.net software). I have one wireless router (AP) in one
location, and the public wifi works just fine with one router, but for full
coverage of the entire campus, I have to broadcast through two physical
concrete firewalls to another wireless router (AP). Signal is weak to the
second router as expected.

In the end, I would like to wire the two wireless points together. I have
two separate CAT 5 runs to both wireless AP locations, so they can
terminate next to the DHCP server...OR...I can run the cable from the
distant AP to the close AP, and then, of course, have the cable from the
close AP to the DHCP server. Ideally, I'd like them both to terminate in
the server room.

I've understand that I'll need a switch to connect the two routers, and
that's not a problem. My question is how do I set up the distant AP with
regards to its SSID and channel. Can I set up both APs with the SAME SSID
(ideal in this case) but different channels? Do they need to be on the
same channels? Do they need different SSIDs?

Bottom line...if I wish to wire the two APs together, what is the best way
to do so to provide the most coverage, bandwidth and mobility. Security is
not an issue...users will get completely unencrypted service.

Thanks!
--Jim