Linux server backup to Amazon S3 (refinements)

We have S3 backups happening daily, weekly and monthly. To save storage on Amazon S3, we would like to modify the existing scripts to compare the latest backup to backups taken on the previous day and only transfer new files to the S3 service when changes happen. We would also like to exclude a folder name from the current backups (as log files don't need to be backed up). Additionally, we would like to add a backup of key system files in case something happens to the server.