Just to jot it down lest I forget:

Tar’ing the local directory and streaming the tarball straight to gzip:

tar cvf - . | gzip > target.tar.gz

MySQLdump’ing directly to gzip:

mysqldump --opt --single-transaction -h HOST -u  USER -pPASS DATABASENAME| gzip > OUTPUT.sql.gz

Using --single-transaction above to avoid locking restrictions on the tables, and it’s more efficient than --lock-tables=false. In large database situations, though, just replicate…

To add a timestamp:

NOW="$(date +"%Y-%m-%d")"

and use $NOW as part of the filename

for example as single line (or just #!/bin/bash) it

NOW="$(date +"%Y-%m-%d")" && tar cvf - . | gzip > target_$NOW.tar.gz)

But you knew that already…