Aged cheeses do best. I prefer an aged gouda for flavor but aged cheddars also work very well even in summertime temperatures. You can't beat some sliced gouda, a few crackers or a hard roll and a glass of port wine while you wait for your dinner to re-hydrate. In a similar vein, parmesan works well but is not exactly a good cheese for crackers/bread - more for seasoning dishes with its salty flavor. A good rule of thumb is that the harder the cheese is, the longer it will last so cream cheese, brie, blue, etc. don't have the warm-weather shelf life that harder cheeses do. I personally am not a big fan of the baybels...too much like a processed cheese in their texture and flavor.
There are many resources on the internet for storing cheese but you don't have to go through multiple steps such as soaking in vinegar, sealing in wax, etc. Just wrap the cheese in a paper (not newspaper, more like butcher's paper) and you should be good to go for many days. Store the cheese in the center of your food bag and keep it in a cool location out of direct sunlight whenever possible.