I use my (delicious!) bread from the bread machine (see here
if you want details). It's about 60-40 white/whole-wheat flour, a nice balance.
For cheese, I use a sharp white cheddar, like Cabot.
Before grilling, I put some kind of spicy brown mustard on the bread, lay down the cheese layer, then add a generous serving of sauerkraut
Something about the onset of winter makes a grilled cheese sandwich sound even more appealing.