Technically, GNOME is a X-windows management system. It is used, by default, as the window manager by all Fedora distributions, although there are "spins" available that replace that default by some other window manager.
In any case, once you have Fedora (or, for what it's worth, almost any other distribution), you can download and install any window manager you want to use. After the X-server starts, when the user log-in screen is displayed, there us usually a "menu" option somewhere on the screen. Clicking that will let you access a sub-menu where you can select from the list of alternative window managers you've got installed.
For example, on this laptop I have a choice between GNOME, KDE, XFCE, Karmen, ICE, Metacity, TWM, WindowMaker, Flubox, and FVWM. (Not that I actually use all of those for much except to play with.)
So. bottom line: pick your distribution first, worry about the window manager later.
A brief word about Fedora: You should be aware that Fedora is, essentially, a beta-test site for Red Hat's commercial offerings. It has a very short release cycle (about every six months), and drops support for any distribution except the current one and that one's predecessor a month after a new release is made. Thus Fedora application are often very close to the "bleeding edge" of development, and never far from the "cutting edge." If you go with Fedora, you should expecte to find fairly frequent technical issues that you'll need to be able to solve. And, of course, you are expected to make reports of bugs to Red Hat when you find them.
That being said, Fedora is my favorite distribution, and the one I use most often.