Advice on extending Airport network

I'd connect all three to powerline and run in roaming mode, much faster than extender.

 

you can daisy chain them wirelessly, but...
wirelessly extending will cut into your network speed, as the repeater has to talk to both the main base, and your computer at the same time. and if you're coming off the second repeater, your speed will be cut again.

hardwire ethernet would be the best option to get to the remote bases, with power line networking being second.

I'm not sure what would happen if you added powerline to the far express, and kept the middle express as an extender. I'm guessing the middle would just pick the stronger signal and join that one.

For the most robust system, I would get 3 powerline adapters, and run both remote expresses off of them. give all 3 airports the same network name and security settings, but different channels and your devices will switch in the background to the strongest signal as you move around the house.
(also put the expresses in bridge mode)

 

Given the better range you get from the Extreme have you considered swapping the positions. Express in the front and Extreme in the center.

 

I've seen very few houses where network cables can't be run between locations. Sometimes it seems like a Rube Goldberg layout but it works. In my previous house I had to run cables up the wall into the attic, over to a closet, down through the closet into another closet then to the basement. Across the basement and up the wall to the printer.

 

This...

Even better following one of Rube's designs, hire an electrician. A professional electrician is a master at running wires unobtrusively and with respect for your property.

The most effective IT money I ever spent was to hire an electrician to run CAT-5 from the cable drop downstairs to the upstairs room on the opposite end of the house. In the last 11 years, I've replaced every piece of tech equipment (computers, switches and wifi routers) but that line of wire.

Well worth the $200 it cost.