I have heard that basically two streams of Linux distributions exists
There are three categories - source code based, .deb based, and .rpm based. The main difference is the packaging method used for applications.
1) source code based - must be compiled in order to install. Dependency resolution is a manual process.
2) .rpm based - use the rpm package management. Dependencies can be satisfied automatically if the dependencies are in the package repository.
3) .deb based - use the Debian package management tools (dpkg, apt, Aptitude, and Synaptic). Dependency resolution is automatic if the dependent packages are in the repository.
For your second and third questions, point your browser at distrowatch.com. On the right side panel, you will find a listing of the top 100 distros, ranked in order of popularity. There is also a Search (at the top of the page) which you can use to find distros by category (netbook, server, etc).