first thing you should do is make sure it works before you go away. you should also consider using a free DNS service like dyndns.org to resolve your dynamic IP address. you can sign up for a free account. if your ip address changes you are locked out unless someone else can tell you the new quad number.
you run a ip updater client (like dyn_DNS_5.exe) on your remote machine, anytime the ip address changes it logs onto your dyndns account and tells them the new ip. all you would enter for remote desktop is: regeisle.dyndns.com instead of 192.358.38.49
to do what you want there are 2 choices, either have your machine standby mode or enable WOL wake -on-LAN support within your BIOS. your network card needs to also support this feature for WOL to work. when you hibernate that is the same thing as shutting it down, so it will not work.
WOL allows your computer to be shut down, while your motherboard provides 5volt standby power. when your network card detects an connection activity it will power on the machine and the operating system will accept your remote connection. WOL acts as a remote power -on switch.
test everything before you go to make sue it works.