How to organize a expedition to the wilderness? How many people to bring?

I am writing a story where the characters venture to a wilderness with some monsters, trying to find a place. I don't know how many people such a group should contain and what kind of things they should be able to do? This world has magic and I understand the fantastic element makes it harder to guess so I am trying to model it as basically a "normal" expedition to somewhere unexplored where they don't want to bring too many people so as to not attract too much attention.

There are currently 4 named characters in the story that are definitely going to be part of the adventure and the rest are going to be NP Cs.

Well, first of all, expeditions require supplies, food and water enough for quite a while. Just a few people can eat and drink surprisingly much given time and a need to move around a lot. Having large amounts of supplies is even more important when the stuff found in the wilderness can be unsafe to eat or drink (plenty of berries and mushrooms are poisonous, and just because the local animals can handle the microbes in the water doesn't mean a random person from elsewhere doesn't get sick) Some means of shelter, such as tents, or a way to make a shelter out of materials found in the wilderness, are also crucial. Sleeping under an open sky in a bedroll or something sounds great, but doing that when there's a chance of rain is just begging to get sick, or at the very least sleep very uncomfortably. Something that one can make a fire with is also needed. If we are talking of an area with dense vegetation, tools like machetes or similar blades for clearing a path will be needed, plus a couple spares in case one breaks. Extra clothes in case the weather changes, or some other factor makes additional/alternative clothing a necessity. Medical supplies of at least first aid levels are needed in case there's an accident.

Then there's the issue of transporting all of this. IRL horses, donkeys, camels, and other similar domesticated animals were popular for this purpose, and a cart could be used for transporting even more stuff. If the expedition follows a river, the pack animals and carts can be forgotten in favour of boats. Alternatively, hiring people specifically for the purpose of carrying the expedition's stuff was a popular approach of historical real life expeditions.

As for how many people the expedition needs....well, even those four people might make for an expedition by themselves. Of course, nobody sets off into the wilderness alone (not for an expedition, at least) and at least a small group is needed....but expeditions don't need to have that many people. In fact, a small group is better, as they need less supplies and can move faster. And beneficial to your case, attract far less attention. However, they need to be able to carry all the necessary stuff and have at the very least basic survival skills (able to create a makeshift shelter, recognise edible stuff and whether or not water found there is safe to drink, recognise possible dangers and be able to deal with them in a worst-case situation, light a fire, etc..) in order to actually survive the trip there and back, and have at least some kind of idea as to where exactly they're headed. If not, they need people who can do all of this. In this case, the smartest move is to get an experienced guide who can take care of the group. Possibly two or even three.

And this is all without counting in any significant threat of aggressive predators, poisonous insects and/or snakes, or contracting deadly diseases. With those, the expedition needs weapons and a lot more medical supplies, most importantly antidotes. Then we get to the dangers of the fantasy setting, which are in your hands.

Depends on the tech level. Back in the day on Earth, when trekking into an unknown wilderness hunting for giant dangerous game was still a thing, a small group (2-4) professional level hunters needed several dozen bearers and sundry other support personnel. Carrying everything you need to survive for several weeks into the wilderness was no small undertaking. A really great description of an expedition like that is The River of Doubt: Theodore Rooseveldt's Darkest Journey, which describes in great detail how Roosevelt and a unit of the Brazilian army traveled the length of an uncharted river.

Movie depictions of a safari in Africa always seem to include a lot of luxury items that you could certainly do without, like the fine china and wine glasses. Use tin plates and cups, and you won't need a dozen porters to carry all that fragile stuff that must be carefully packed and handled with extreme care.

I think the most important factor is time. What a group of people take into the wilderness depends on the amount of time they want to spend.

For example a short trip of a day does not need any equipment for the night, but longer than a day and it is going to be necessary.

Food is also dependent on time. If they are only venturing out for few hours, no food necessary. If it is a expedition of a few days you need to pack some nourishment, but if it is going longer than a week maybe it is more wise to let go of food and equip tools for hunting and acquiring food on site.

Aside from that maybe considering the space, by that I mean the geography and environment. A snowy mountain needs different equipment than let's say the hot desert.

I hope this can help.

If it's uncharted, unsettled wilderness, then the rule is "If you dont take it, you'll need it, and there will be no way to get it." That means taking spares of everything- clothes, food, utensils, weapons, ammunition, medical supplies, tools for wood, metal and leather working, shelter, waterproofing, mapmaking, sample collecting, and even heavy tools like shovels and saws. If dray animals are part of this, then all the supplies necessary to support them as well. It adds up quickly.