Just about every router being sold nowadays is designed for wireless operation, so I'm not sure what you mean by a "wired" router. You might want to consider an Airport Extreme unit instead of using your Airport Express and an additional router. The Extreme will accommodate an external USB drive for Time Machine, and provide a wireless signal.
I had it going via hacks a while back, but it scares the heck out of me if I had to do a system restore via TM. Is there a way to verify a TM backup that is taken with a "workaround?"
Personally i would avoid the Time Capsule for a couple reasons:
a) TC comes with either a 500GB or 1TB drive. Once you fill it up you have no option to replace the drive with a bigger one.
b) If you ever want to take your backup drive off site, you have to take the whole device which means taking down your wired and wireless network.
If you buy the Airport Extreme Base Station and a USB HD you can change out the HD any time you want, and can easily move your backup offsite without having to take down the entire router.
I've also had absolutely no problems using Time Machine to backup to my USB HD connected via AEBS.
Shop for your Apple, Mac, iPhone and other computer products on Amazon.
We are a participant in the Amazon Services LLC Associates Program, an affiliate program designed to provide a means for us to earn fees by linking to Amazon and affiliated sites.