Exchange Server

We are a group of MCSA and we are trying to install and configure Microsoft Exchange Server 2007 at our own. We are succeeded and at this point we are able to send and receive mails locally. But we are still unable to send and receive mails outside LAN.

Our Scenario consists of
1. One Domain Controller + DNS
2. One Exchange Server
3. One Client
4. One ISP router with fix public IP.

We have registered a domain name with strangerz.net and created A and MX record for our domain with SMTP port open.

What we need to do further for sending and receiving mails

Shall we connect our exchange server directly to the internet or our domain controller.

Do we need to configure our local DNS server for mail records.