Hi, sorry for the not really what you want to hear reply
Backing up mysql and app files to a tar file is reasonably easy, as is restoring them. However incremental backups into tar will be tricky. The script will likely either be complex or too basic and fiddly. If this is a school project or similar basic and fiddly would likely be ok heh.
Much *nux backup software will have command line access to it's functions and will be able to cope with mysql data and the propriety ones will likely also have incremental backups. I doubt very much that you're going to get incremental backups to tar using a script written here for free, I certainly do not have the time, sorry.
If someone else does that's great, indeed they could then publish it to a website under GPL and everyone could use it...oh yeah several people already have and they're searchable for on google
The following are some basic pointers, if you wish to have a go at writing it yourself I'll attempt to help with problems you encounter.
You can use mysqldump to backup mysql data;http://dev.mysql.com/doc/refman/5.1/en/mysqldump.html
You can restore mysql data using the dumped backup and piping it into mysql client similar to this;
mysql < backup.sql
To tar files up;
tar czf backup.tgz files/
To restore the tar files;
tar xzf backup.tgz
To copy to another server;
scp backup.tgz my.backup.server:/backup/location/