Mini towers are great for a space saving solutions and for use with Micro ATX and Flex ATX motherboards. Like desktop enclosures, mini towers are also good for systems that have many integrated features. The typical user would not choose a mini tower unless they are going to have a small number of devices attached to their system. Mini towers come in the AT and ATX form factor varieties as well. Medium towers are the standard chassis for most home computer systems.
Medium towers come in many different varieties of styles and colors.
Medium towers come with more expansion bays variances than other types of towers and enclosures. If you are truly confused as to what sort of enclosure would be best for you, then a medium tower case would probably be your safest bet. Server chassis are largely varied in their functionality and offer a wide variety of choices to system integrators and end users alike. Rack mounts are primarily used for server solutions and not typical for the end user. Rack mounts also come in a variety of sizes and can vary greatly in what solution they are used for.