Time Machine backup to remote disk at night
To schedule your Mac to boot or wake up at a particular time every day, you can use the Terminal command pmset. In your case, the appropriate pmset command would be: 

pmset repeat wakeorpoweron MTWRFSU 02:58:00


To schedule Time Machine backups on crucial servers after hours, I've relied on TimeMachineEditor. With this app, you can set backups in a very granular fashion.