|IIS will enable you to host a website.|
Install it from Add/Remove programs --> Windows components.
Buy a domain name and point it to your Static internet IP address. If your Internet address isn't static, you will need to register a host name at dyndns.org (free). Dyndns will act as a middle man and every time your internet IP changes it will update their dns record.
Now your domain name will always point to example.dyndns.org
Example.dyndns.org will point to the most recent ip held on dyndns's system.
You will need to make sure this server machine has a static IP that you can set your router to forward port 80(unsecured) or port 443(SSL encrypted) to.
IIS supports allot of web page extensions, plus you can add extra extensions on. I personally like .php which connects to a mySQL database just nicely.
Unfortunately i cannot help on connecting a web page to a database. However as far as i am aware, it is the webpage's that you need to program with tthe database connections. (IP address for the Database server, User name, & password).