Is it beneficial to use an Airport Express's wifi instead of my modems? I have a modem/router that came with my ISP and I have two Airport Express.  I have the Airports so I can extend my signal further.

My current setup is:
Modem -> ethernet -> Airport Express 1      -> wireless ->    Airport Express 2.

On the Airport Express 1 - I can either create a new wireless network for AE2 to connect to, or I can join the modems connection.

What advantages / disadvantages do I have to creating a new wireless network on AE1 vs. joining the existing one from the modem?
The advantage is you can locate the airport potentially closer to you than the modem. The disadvantage is you need to set it up and perhaps string an ethernet if you wish to avoid delays of wirelessly extending a network.

If I could, I would always run an ethernet cable (gigabit if possible, but 100 is usually faster than any WiFi consumers use in practice) from the router to all base stations.

That allows you to choose different channels and devote 100% of the wireless bandwidth to serving clients as opposed to backhauling traffic to the router.