Warning: This is a work in progress, there may be formatting and other errors. Please add webservers, addons, you like or use. Feel free to correct typos, grammar etc.
-TTT_Travis

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Introduction

There is several different ways to run a web server. Below I will list several different ways to run a webserver on your home computer. Remeber if your running a webserver your computer must be on for your site to be up.

Running Personal Site

If you just want to run a site with HTML pages, you may just want to download and install a copy of Abyss Web Server, its a very small, free download. Abyss is extremely easy to install, setup and use, perfect choice if you are new too running a web server. Abyss can also be configured to run PHP, ASP, Perl and MySQL very easily by following the guides on there website. Abyss is available on Windows, Mac OS X, and Linux.

Running a Bigger Site

If you want to run a bigger site with PHP, Perl, and/or MySQL but you aren’t very comfortable with setting up any of it, the solution for you is XAMPP. Apache Friend’s XAMPP is available on Windows, Mac OS X, Linux and Solaris. XAMPP is a pre-configured package containing a small mail server, Apache web server, Filezilla ftp server, PHP, Perl, MySQL and much more in 1 easy to setup and use package. XAMPP is very easy to use and is the definite choice for anyone who wants to run a web server.

Setting Up a Site Manually

Alternatively, you may want to do everything manually. First, figure out what you want your server to run. Once you figure out what you want to run download, install, and configure extra addons like PHP.
Here is a list of recommendations.

Servers:

Apache Web Server
Price: Free
A very popular web server that powers over 68% of the internet. Very strong and stable. If you are not comfortable with using a text editor to configure your web server this is probably not the web server for you.

Abyss Web Server
Price: Free
Another very good web server, not as well known as apache but just as good if not better. Unlike apache, configuration is very easy via the graphical control panel. This is by far one of the best web servers out there for small personal sites.

Abyss Web Server Professional
Price: $59.95
This is made by the same people that make Abyss Web Server. This is the professional non-free version of the software. Its just as easy to use as Abyss with TONS of features. Fine choice if your running a large site and don’t want to configure apache by hand.

Filezilla FTP Server
Price: Free
Awesome free FTP server not much to say about it does what it says. Filled with features and loads of extras.

Addons:

PHP
Price: Free
If you want to run any PHP scripts you’ll need this. Allot of forums and blogs aswell as thousands of other scripts are written in PHP. This is also included with XAMPP.

ActivePerl
Price: Free
This allows you to runs Perl/CGI Scripts. This is also included with XAMPP.

MySQL
Price: Free
The most common database software. This is used by some PHP scripts to store information. If you want to run a blog, forum, or CMS you’ll probably need this. This is also included with XAMPP.

Getting Scripts

Most scripts can be found at HotScripts. If you know any of the languages (PHP, Perl, CGI, Java, ASP etc.) you can submit your own scripts there.

Here are some well known scripts for doing many things.

Blogging
A blog is used to write thoughts news to family friends, or anyone. Check out Leo’s blog.

Word Press
Price: Free
Word Press is one of the most commonly used blogging scripts. Its feature rich and pure awesome. This most likely the best way todo a blog.

pMachine ExpressionEngine
Price: Non-commercial License $149.95 - Commecial License $199.95
This is actually a CMS, but it can be used as a blog. This is what Leo Laporte and Kevin Rose for there blogs. I haven’t tried this, if you have please post what you think of it.

Content Management System (AKA CMS)

e107
Price: Free
My personal favorite CMS, full of features, themeing is pretty easy if you know some basic PHP, and if you don’t you can just get some themes from e107 Styles, you can also submit your own themes. This in my opinion is the best CMS. There is also hundreads of plugins to make it do anything you want at e107 Coders. They also let you remove/change the disclaimer without paying a license fee.

PHP-Nuke
Price: Free
One of the most well known CMSs very feature filled, not my favorite because its not as customizable as e107, but worth trying.

Feel free to add to the list.

More Info

For more info on running your own webserver check out DIY Webserver