Last Christmas, I helped Santa deliver my wife and I emergency/get home bags (GHBs) for the cars, each set to handle 1 adult and 2 kids -- which (un)surprisingly double as light backpacking/hiking kits. We've used them a number of times on day hikes to good effect, so there should be some overlap with what you need. Based on figuring out what we needed for those, and my hiking and camping experiences, here is my input:
Since you did not mention a budget other than "low price", I'll jump in with a few good, solid recommendations that are inexpensive, but good deals for the quality at a low price point.
For fixed blades:
- Mora ($10+) - the Robust can take a bit of a beating and the Companion is a great deal, and there are higher budget options too, so whichever type you like. I opted for Moras in the GHBs because they work and are easy to sharpen. We also have a number of them around the house dedicated for specific tasks, like the one in the fire pit kindling box and the one in the cabinet next to the fireplace and the one in the hose project toolkit, so we are used to using them.
- A.G Russell Woodswalker ($15-30, depending on sheath) - not a super steel, but a decent small knife - think paring knife sized. My seven year old daughter has been using one for recent camping trips, hikes, and backyard fires (like this afternoon) along with a small Vic she got for her last birthday. The woodswalker is still mine, but she can borrow it if she asks and has been behaving. If she continues to show she is (mostly) responsible, it'll be hers by Christmas.
. It is a very pocketable knife in the leather sheath. I don't like neck knives, but the kydex sheath for it works well too.
- War Eagle Blades Pocket Skinner ($15)- bigger than the woodswalker, but again, a decent inexpensive blade, but the sheath has no way to attach to a pack or belt.
- I'll add the A.G. Russell Hunter Scalpel for giggles. My five year old son has been using one under close supervision for fire prep and it has been in his backpack on hikes and camping trips, because big sister has the Woodswalker. It's too small for my hands, but is the right size for him, and I like the sheath lock on it for a kid's knife.
For folders (not included in our GHBs since I always have at least 2 knives, and my wife has a Delica or Dragonfly on her):
- Spyderco Persistence ($35ish) - decent budget one handed folder, and my backup when I can't carry a fixed blade.
- Victorinox Swiss Army ($20 -> whatever) - It's a blooming Swiss army knife, you can't go wrong with one, unless you need a corkscrew and opted for the phillips instead..... not that that has ever happened.
I always have an alox farmer and a classic in my pocket, no matter what else I carry.
- Spyderco Delica or Dragonfly -- if you can swing 4 of either of them in the budget, my wife loves both of hers

I personally would do 2 knives per person - 1 dedicated for food, 1 for wood processing and anything else that comes up. Why? I have heard/read a few horror stories about nasty fungi and things getting into food from a knife that was "wiped clean." 2 color coded Moras could be an inexpensive option, or a mora and a woodswalker. And with 4 daughters, you could personalize the knife combos a little with this approach.
For saws:
I had a silky pocket boy saw. Then my wife saw it, and stole it. Now, we have 3: one in each GHB and one in the garage (the original) that I have to ask permission to use if I don't want to be in the dog house. YMMV.
Don't forget a small whetstone, DMT card, or ceramic rods so they can keep the blades touched up. Just make sure they can use it.
And a
trauma kit (quick clot, gauze pads, Israeli bandage, ace wrap, and Sam splint type stuff ... because bad things happen).
And a
first aid kit (bandaids, advil, bug bite cream, and moleskins . . . because blisters and small cuts stink), and you should be set.
Good luck and enjoy.