What are the best options for cheese? WhAt varieties last longest?

Your best options are harder aged cheeses but in reality if your only out a week even softer cheeses like Cheddar/Jack will keep. We like Gouda and Gruyere on our meat and cheese days with some nice summer sausage or salami.

Hex

I've taken cheddar blocks on trips. They get oily when they get warm but they're still fine. Most popular on our trips are cheese sticks, which will last about a week outside of the fridge if you take care to keep them out of direct sunlight as best as possible.

I've never had cheese go bad. That includes extra sharp cheddar out for a week plus. Cheddar does "sweat" but I haven't had it get moldy. In hot weather, I keep my cheese in a "swamp cooler" made out of an old blue jean leg which gets dunked in the lake and then hung in the shade when we get into camp.

For long trips I have heard of taking blocks of cheese and wrapping them with cheese cloth dampened in vinegar and then dipping them in wax.

I have also taken gouda that comes in a small wax wrapped block and those can ride around in the pack for a long time before anything would happen to them.

Personally I like the flavor of warm cheese.

For lunches we like the Baby Bel individual wax-enclosed cheeses. The wax wrappers make great fire-starters later, too.

I usually take 3 or 4 kinds - cheddar, swiss, parm, muenster, gouda, even brie...all are fine for a week or two. Some do get oily but still taste fine.