I think it's interesting to clear one thing up, Digital Ocean offers Droplet automatic (and manual) backup, but you shouldn't rely on it for the data backup (auto: because it runs just once each 3 days or so, manual: because you may forget and it won't run as often as you would want). DO's backup should be used only for having a fast way to recreate your droplet if anything goes wrong, then on top of that you restore your database, files or anything that changed between the backup and the failure.
Right now I'm using a custom .sh script:
#!/bin/sh
echo '\n'
echo '******************** BEGIN ********************'
echo "Begin $(date)\n"
FILE=backup_`date +%Y-%m-%d_%H-%M`.sql.gz
MYSQL_PASSWORD="mysqlpassword"
cd ~/backups
mysqldump -u mysqluser -p"${MYSQL_PASSWORD}" mysqldatabase | gzip > ${FILE}
echo "Backup done! Sending it to backup server\n"
scp ${FILE} user@host:~/backups/database/
md5sum ${FILE}
rm ${FILE}
echo "\nEnd $(date)"
echo '********************* END *********************'
That runs on cron 4 times a day, but I would like to change this to incremental backups, making 1 backup per day + incremental backups each... I don't know, hour? But I didn't figure a nice way to do this :(