Apache is a good choice for hosting websites over the intranet(LAN) as well as over the internet. Most of the companies use Apache for to host their websites.
Install it using the following command:
sudo apt-get install apache2
And copy your website folder to /var/www.
sudo cp /path/to/website/folder /var/www
Now head over to your browser and open the url http://localhost/websitefolder.
Don't forget to replace websitefolder with the name of your website's folder in /var/www.
To access the website from a different device over the LAN, you need to find out your Local IP address.
Here's how to find it out. Type the following command in the terminal:
ifconfig
Once you know the IP address head over to http://ipaddress/websitefolder using the device's web browser.
Also, regarding the database MySQL and PHP will be an ideal choice for beginning.
Install them using the following commands:
sudo apt-get install php5 libapache2-mod-php5 mysql-server mysql-client
If you want to access the MySQL database using a web interface install phpMyAdmin alongside.
sudo apt-get install phpmyadmin
Don't forget the restart the Apache web server to make everything work perfect.
sudo /etc/init.d/apache2 restart