Mac – Airport Extreme + USB Drive vs Time Capsule

As above the Time Capsule is the easy solution.

I can only really comment on your second point, I bought one about 3 years ago and 18 months ago the hard drive failed, it seemed to be a known problem as Apple replaced the Time Capsule free of charge even though it was outside of the warranty period. What could not be replaced however was the 18 months of backups as Apple would not have replaced the Time Capsule had I opened it up to get a the drive and try to recover the data. So after that experience I won't be buying another Time Capsule.

If you are not particularly after a router there are now other companies that offer Time Machine compatible network storage, which may be worth looking at.

If the old Airport Express was connected directly to your cable/DSL modem and the new Time Capsule replaced it (again, directly connected), you may need to reboot the modem (generally by unplugging it and plugging it back in, maybe holding down the reset button) to reset its DHCP. You may also need to do this in a particular order, generally 1) shutdown Time Capsule, 2) reboot modem, and 3) restart Time Capsule.

Reason: some broadband modems seem to only assign one internal IP at a time and only check for a device on startup.