Cooking Raw Meat in a Campfire does work fine. It is a bit slow, but the campfire will cook 1 piece at a time. If you want to cook meat faster, then you will need to use multiple Campfires or an Industrial Grill. The Industrial Grill will cook as many as 13 pieces of Raw Meat at a time.
To preserve your cooked meat you have a few options. The first one is the Preserving Bin, which is fueled with Sparkpowder. You can also add Oil to the Preserving Bin to create Meat Jerky.
The Fridge is the best way to preserve things. Keep in mind that while putting cooked meat in the Fridge will make it last much longer, Meat Jerky will last even longer in the Fridge than Cooked Meat. Also keep in mind that if you don't have a Fridge you can still extend the life of your Meat Jerky by putting it in the Preserving Bin.