This question is asked alot yet I can't seem to find any good examples in search...(weird)
If you have never seen Linux:
1 Try Knoppix.. It's a "Live" Cd it will run from your cd drive. No install to hard drive.(if you don't want to that is.)
If are new to Linux and want an experience similar to WIN
I have not installed all of these, but most are on the easier side to install and get working.
If you are proficient with computers and are not afraid to do a little reading:
1. Fedora Core 4 (good installer, free version of Red Hat, great tools, a lot of reference material,etc..)
2. Slackware ( my favorite distro. I have tried a lot of distros, but this is the one I am most loyal to.( I always come back to Slack)
*installer is not the most user friendly but it is solid as a rock.
3.Debian - Everyone at the LUG I go to uses it. I've never tried it. They are kinda cultish about it.
4. Arch - Very solid L33t linux distro.
From your list.
RedHat- you have to pay for. A good business(enterprise) distro.
Mandrake- A good newb distro. The free version seems to nag you to get the pay version.(my opinion.)
Slackware- Again my favorite. Very solid distro. Most people have a love/hate feeling toward it. A good learning distro.
Vector similar to Slack, but better on older hardware.
Check out Linux.org and go to distributions tab. You can look through a bunch there.
Distrowatch.com will give you an idea of the distros and their popularity.
as stated above look at RUTE:
My progression through distros has been:
Knoppix-->Suse 9.0--> Slackware--> Fedora-->Ubuntu-->Gentoo
I have tried many more but these are the ones I actuall "used".
I hope this helps.