When we make these at home we use pickled jalapeno peppers. I think the extra acidity sets off the rich filling nicely. We picked that trick up from the Bit & Spur, which used to be a pretty good Mexican place outside Zion NP in Springdale UT. It might still be, just haven't been there for a few years.
Cheese is kind of your choice, but I agree with others that you don't want something that will break and get too oily. Mexican cheeses work well, as do mixes of cream cheese and cheddar.
We like to top them with a little red sauce (like an enchilada sauce).
At home we usually broil these, and haven't tried to cook them on the trail. I'd suppose a heavy skillet with a good fitting lid that was preheated might work well. I'm sure you could use a dutch oven, but that's a lot of work for what should be a relatively simple appetizer.