Most distros offer a choice of "desktop environments" and/or "windows managers."
http://en.wikipedia.org/wiki/Desktop_environment
http://en.wikipedia.org/wiki/X_window_manager
My recommendation is to choose a distribution based on such factors as: stability, size/quality of software repositories, easy install of your favorite applications, quality of support, friendliness of community, frequency of updates, hardware support, philosophy, etc. (whatever factors are most important to you) and then find out if they offer your favorite DE/WM.
Here is a nice comparison of DE's from the Arch wiki:
https://wiki.archlinux.org/index.php...op_Environment
Here is a good comparison of the top 10 distros:
http://distrowatch.com/dwres.php?resource=major
You have some good suggestions, so I recommend to create some Live USB's and take a few of the recommended distros for a test drive.