First goto justhosts.com (or any other webhosting company) and register a domain name. Then you can now have two scenarios a) Your exchange server receives mail from internet directly, or b) it pulls mail from your Hosted email accounts using POP3.
The second scenario will be easier for you. Just create email accounts on the Hosted accounts and then configure your exchange to pull mails ( if you have an SBS server the POP3 retrieve software should be included, but if not, you can buy any here.
Then you need to speak with your ISP, it seems you are given a Private IP address which cannot receive or send traffic directly to the internet. They can either give you a smtp relay on their network or perhaps ask you to upgrade and get a Static IP address. The second option will be a bit more costly, but you’ll be able to access your Exchange server from the internet and also configure your VPN.
Server 2003 supports VPN, you can configure it from the RRAS. Detailed information on how to do this is available on the internet.
I think the IP you are looking at comes from an internal router, not your ISP. Run IPconfig/all from a command line and you will see what your isp dns servers IP addresses are. That is the same range they send to your modem. What is connected to your modem? If you have a router like linksys then that is why your IP is 192.168… Yes you must register a domain name to send and receive email from your exchange server. You will also need to create mx records in your DNS.