I personally don't care for red wine with cheese. I don't find it a good pairing. I much prefer white wine with cheese. It all depends on your taste buds, but in my opinion, you want contrasts. What I mean is this; if you've got a dry cheese, you don't want a dry wine with it -- too much dry. If you've got a sweet, buttery cheese, you don't want a sweet buttery wine, too much butter and sweet!
If your cheese is sweet and buttery, like Brie for example, you want a wine with some acid and mineral to cut through, refresh your palate and let the two emphasize the best qualities in each by providing contrast. IMO, a fabulous pairing is a Muscadet. That's Muscadet, not Muscat. Muscat is a sweet dessert wine, Muscadet (moose-ka-day) is a light crisp, minerally white wine from the Loire Valley in France. (This is also a fabulous wine to drink with Oysters!)
You can get great Muscadet for $12 to $20.
Sancerre (Sauvignon Blanc) is another fabulous choice with sweet buttery cheese. I like Sauvignon Blanc from Sancerre because it tends to be crisp and that's what you want.
Champagne will also make a wonderful pairing.
I have never really found a wine that pairs well with a cheese like Sharp Cheddar, so I just don't serve it with wine, I grate it and put it over chili and eat that with a nice Chianti.