A word on food -
If you're exploring, it's usually best to sustain yourself simply by foraging as you go. Pick up any seeds you find along the way, and also the occasional berry or carrot. Just take what you need, though, unless your goal is to bring a lot of food back to camp to cook for others. Berries and such spoil quickly.
You can cook things on an open fire. Usually (but not always) this will make it more beneficial when you eat it (notable exceptions are corn and certain kinds of mushrooms). However, for all the extra work it usually takes to get meat in this game, cooking it over a fire and eating it really doesn't give you much more nutrition than eating berries.
For the best results, you want to use a crockpot. Combining 4 items in a crockpot will cook them into something new. The most basic recipe, and probably the most hunger-efficient, is
meatballs - one small unit of meat, and 3 edible fillers. The fillers can be berries, vegetables, or even ice. This turns a 12.5 hunger meat morsel into a 62.5 hunger dish. Just watch out, if you use frog legs as your meat, and one of your fillers is a vegetable, you'll make a
froggle bunwich instead. This might actually be a valid choice, though, if you need healing - a froggle bunwich only restores 37.5 hunger, but it also heals 20 health.
Keep your ingredients and finished products in a fridge (or even better, each in their own fridge). The freshness of your final product will be the average of the freshness of your ingredients plus a small amount.
Cooking something over a fire also increases its freshness, so if you've got some berries that are very stale, cook them over a fire and then use them in a crock pot.
As for meat, it can be made to last much longer if you hang it from a drying rack. Turning meat into jerky completely refills its freshness, so if you're trying to maximize ingredient longevity, wait for the meat to go stale before you hang it.
Cooking green mushrooms is a really good way to restore sanity. It does a tiny amount of damage, but it's usually worth it.
Taffy is also good for restoring sanity - to make it, put 4 honey in the crock pot. It also does health damage, but since you've obviously got a source of honey, the damage can be mitigated by eating some raw honey as a chaser.
Every character has a "favorite food." They will get bonus hunger restoration from eating it. Find out what it is, then see if you can prioritize making that.
My go-to crock pot recipe is usually
Pierogi. It's like a froggle bunwich on steroids, healing 40 health, 37.5 hunger, and 5 sanity. To make pierogi, combine 1 meat, 1 egg, 1 vegetable, and 1 filler (say, berry or ice) in a crock pot.
Eggs are easy to come by once you have built a bird cage and imprisoned a bird in it - every meat morsel or frog leg you feed the bird will make it immediately produce an egg. If you've got a Wendy in your group, and easy access to frog ponds, you shouldn't have to worry about meat or eggs.
Other good sources of meat:
Gobblers (those giant turkeys that try to steal your berries). These can be outsmarted by simply dropping food on the ground in a fenced area. They will try to go after the food on the ground first, but aren't smart enough to attack the fence. Kill them easily, and get rewarded with 2 turkey legs. These are small meat morsels and can be used as such, or you can combine two turkey legs with a meat (or monster meat) plus one filler to make a
Turkey Dinner.
Monster meat is different from regular meat, in that unless you are Webber, eating monster meat will hurt your health and sanity. Using monster meat (or monster jerky) in a recipe however is safe so long as you only ever use 1 monster item in the recipe (and durian counts as a monster item). So, one monster meat and 3 ice will still make completely safe meatballs, but using more than one monster meat in a recipe will get you Monster Lasagne, which is of no use to anybody but Webber, and even then it's kind of a waste.