Sounds like a perfectly reasonable plan. The Extreme is a very capable router and the Airport Express (the plug adapter) works well to extend Airport-based wifi networks.

A few things to note:
1. Ethernet over power adapters have to be used in pairs and while they can work very well you won't know how they perform until you get then in-situ (much depends on how the wiring is configured in the house).
2. I don't know the nature of the issues you're currently having but you need to consider channel clashes with nearby wireless networks, house construction and interference - a new router may not necessarily be a silver bullet to resolving all of those issues.

There are other routers to consider but the majority of my recommendations would be ADSL modem/routers so perhaps a member with greater cable modem experience can through a few ideas your way.