Have a look at Simple, Secure Backups for Linux with rsync
basically, it's rysnc <source> <destination>:/path/to/save
There are 100s of options as you will soon see. None, In My Opinion, there is no "best" or "fastest" as conditions such as environment, throughput, memory, filesize all have a contributing affect on the job.
As for retries, never seen that and I'm pretty sure that rsync has some internal mechanism for assessing latent file write operations. Others here may have insight to that.
I do know that rsync uses hashes at both ends to determine if
the file got written correctly.
hope that helps.