If I'm understanding your question, You can have both KDE and Gnome when installing Red Hat 9. If you have the drive space for it, I've found the best way to install first time is to install everything. The RH 9 install will give you that option. Fedora, Mandrake, Redhat 9, and many modern distros have a pretty straight forward graphical installation, which to me, is easier than a Windows install. I wouldn't reccommend trying to install Debian if this is your first attempt. It's a text based install and not easy. I've tried to install Debian 5 times and finally gave up!
 
Even with a graphical install, it may take 2 or three tries until you get your system set up the way you want it. Be sure to create a seperate partition for /home, so you can save your valuable files and preferences there from install to install.

When you install red hat or mandrake, KDE and Gnome are different... For example in red hat it has a diferent background and it has a hat in root's home. I would like to install a distro with the options by default, with the default background.

If you install RH 9, and choose the option to install everything, you willl then be installing both Gnome and KDE. On first boot, the log in screen will come up, giving you the option of using either the Gnome or the KDE desktop environment. Both have a lot of the same and a lot of different options and programs. You can easily run the background image of your choice with both.

The differences you mention are built in to KDE and Gnome. The hat is Redhat's trademark. You will get something different with Mandrake, SuSE, Debian, et al. There is no 'default' Linux background, icons, etc. You may not be able to make KDE look the same as Gnome or vice versa. There are themes available for most, if not all the window managers. Google for "KDE themes" or "Gnome themes" or even "Linux themes" these themes will change the entire look and feel of the GUI. You can change most or all of these things manually, but I can't tell you where to find the way to do it. ;(