X11 tunnelling over SSH works fine over a local network (it's like sitting at the console over gigabit)-- that's actually how I work on a daily basis; Eclipse or jEdit running on the remote machine to which I'm connected over SSH. Install Cygwin's X11 packages (easiest to just install the whole category), start X11 from the start menu, and do ssh -Y username@hostname from the terminal window that appears and you should be able to run graphical applications and have them appear on your local machine.
If you're not on the local network (as in, you're trying to connect over the web) you'll want to use something like XRDP (an RDP server for X11), VNC, or NX. X11 doesn't use a ton of bandwidth itself, but it produces a lot of back-and-forth traffic and therefore runs pretty poorly on a high-latency connection.
On the subject of graphical file managers, either nautilus or konqueror will give you an experience closer to what you're used to. Once you've gotten a graphical connection to your linux box, you'll most likely be able to run one of the two by name (if Gnome or KDE are installed). If you're using VNC or RDP, you should have a destkop visible with one of them already running.