There are numerous reasons why camping and fishing go together like bacon and eggs.
Sometimes the only way to spend much time at a particular lake or stream is to camp there, because there are no other facilities. There was the time, for instance, we were camped up in Montana's East Pioneer Mountains, fishing for grayling. Only way up there was by horseback, and we stayed in a semi-permanent camp put up by an outfitter. Similarly, if you want to fish for the smallmouth bass and pike of the Quetico Superior Wilderness about the only way to do so is to canoe-camp.
Other times finances dictate that you either go camping or you don't go at all. When our kids were small, and money tight, the only way we could afford to fish the confluence region of the Catskills was to camp. It was that or stay home.
And sometimes you camp merely because you like doing so. I can't remember the last time we didn't camp while fishing the Smoky Mountains. And, where legal and feasible, nothing compares to camping on a beach, with the surf pounding outside the tent, and the wolf-packs of blues chasing baitfish to the shore.
What to do with the fish you catch is an open question. As with "why camp?" there are many answers. If you're strictly a catch & release angler the answer is self evident. On the other end of the continuum are fishermen who are there to stock up. They want to fill a cooler or two with filets and fish in the round, which they can take home to freeze. That takes care of their fish requirements for the year.
If you're in that group, you need to learn about various ways of cleaning & prepping fish and freezing fish for the trip home. Considering how many fishermen/campers actually make these once- or twice-a-year trips, it's astounding how many of them do not know the best ways of keeping the catch fresh and wholesome. Super-chilling, for example, makes much more sense, most times, than freezing. Yet very few serious fishermen seem to know about the technique.
Somewhere in the middle is where most of us fit. We fish, while camping, because it's an enjoyable part of the outdoor experience. Maybe we keep a few fish to cook while there. After all, the whole definition of "fresh" changes when the fish comes out of the water and directly into a skillet.
Among other things, this means bringing the skillet with you. The kinds and quantities of cookware you bring depends greatly on the kind of camping you do. Car camping, using campgrounds in a National Forest, means you can carry pretty much what you need, no differently than with an RV in a private campground. There are virtually no restrictions to either, and if a cast-iron Dutch oven is needed, just toss it in the trunk. A pack tent in the backcountry, on the other hand, means just the opposite; with weight and bulk being primary considerations. Camping by boat, or by horseback, puts you somewhere in the middle. You certainly can carry more cookery stuff. But still can't get too carried away.
Size of the group can also determine the cookware. A 12" skillet, for instance, makes cooking fish on an open fire a joy. If it's just one or two or you in a back-country camp, however, toting anything that big is problematical at best. But with a large group it becomes part of the community gear, and you can handle the weight and bulk because others will make up for it.
You should consider a grill rack if fish are going to be on the menu. There is probably more camp fish "broiled" over an open fire than are cooked by any other means. But you do need some way of supporting the fish over the coals. Hikers rarely carry a grill, even a small one. But there's no reason not to, as there are versions made specifically for backpackers.
If you expect to use specialized techniques you have to plan on them before leaving the house. Plank cooking fish has long been part of the camping mythos. It's easy to do, and the results more than worthwhile---providing you thought to bring both the planks and some nails. Otherwise there is no way of pulling that off. By and large you will not find an appropriate piece of wood to use, once in camp. And even if you do (in a pinch, a roughly split limb will work), how will you tack the butterflied fish to it?
Here are a few fish recipes to try in your next camp:
Recipe: Puppy Drum Chowder
Recipe: George River Salmon
Recipe: Bourbon-Curry Bass