You wouldn't have to become a scripting genius to do this.
You can use cron to run your script at the desired times, or simply run it as a login script Though this may slow the machine down for a little bit while you are trying to use it.

You can drop afp servers into your list of login items, then your script would only need to run a cp terminal command or two to copy the required folders onto the network volume. You might be able to do it with automator. Then you can use cron to schedule the backups, or you could attach a shutdown command on the end of the script, then when you feel inclined, finish using the machine, run the script and it will back itself up and shut itself down.

Don't try too hard on this, a family pack of Leopard will do this for you much better with Time Machine. And the server wouldn't need to be running Leopard in order to do it either.