FedoraOS (fedoraproject.org)
A - Apache Web Server (http://httpd.apache.org/)
M- MySQL
P - PHP
Many predesigned scripts for websites use PHP & MySQL. All hosts offer minimum 1 MySQL database & some of them offer a web based interface for editing databases called phpMyAdmin.
CubeCart is an example of a free Shopping Cart Script that requires PHP and MySQL:
FTP Access - Unlimited and unrestricted FTP access to your site is essential. You will need an FTP program to transfer files.
Firefox 3 has an excellent Add-On FTP program called FireFTP.

Control Panel - Not all control panels are the same. Some are easier to use than others. Some control panels the learning curve is steep while others are easy. The best (& the most expensive) control panel is cPanel (www.cpanel.net) which costs $1500 for a single server license. It is extremely easy to use & has a lot of helpful add-ons. For example , there is Fantastico AutoInstaller from Netenberg , which installs blogging softwares, shopping carts & many other softwares in 3 steps.
Statistics Program - A good stats program is handy if you want to keep an eye on how many visitors you are getting, where they are coming from, referrers, top entry and exit pages and so on. Some companies offer excellent stats programs as standard. AWStats is an excellent FREE advanced statistics program: . AwStats comes preinstalled with cPanel.

An easy way to test your potential web host is as follows -
1.) Go to Google, & search for - "WebHost Sucks" (e.g. LaceHost sucks , though it doesn't )
2.) Search for "WebHost down".
This gets you most of the -ve reviews
3.) WebHost reviews - gets you the +ve & -ve reviews.
4.) WebHost testimonials - gets you the +ve (but sometimes forged) testimonials.