Ali,
This design/what you are trying to do is quite normal, I have a few questions:-
1) What speed is the connection from the HQ to the internet, it would ideally be 1.5mbs or higher?
2) Would internet access from the remote sites be required to pass thru the HQ?
3) Are running VoIP - you need to define a QoS policy
4) Are the remote sites going to have static Internet IP's or Dynamic?
5) Will the HQ have a static IP internet address? This is a must.
6) Are you currently running any dynamic routing protocols? if so you need to have GRE tunnels.
HTH>