What setup is needed to stay backed up and online after retiring the TimeCapsule?
You could certainly try backing up to a computer running a server version of the OS which allows for networked TM backups to it much like your Time Capsule.

You could also just get an Airport Extreme and roll your own Time Capsule equivalent.

You could try to nail the performance issues of you TC by attaching wired to see if things improve, and it may then prove simplest to just improve your Wireless capabilities by wiring a couple of cheap Airport Expresses to it, you could then even though a cheap switch on the end of one for faster backups if you have a large one.