Good question. Like a personal med kit I would recommend getting some training to help you guide your purchasing/procurement.
Doing a solid threat assessment of what you think you will need to be prepared to treat is going to be a major component. Your environment may pose some specific threats that you may need plan for when building your kit i.e. ORS/rehydration salts for hot areas, etc.
I will break down my recommendations by the types of injuries you mentioned:
Larger cuts:
-5x9 gauze
-4x4 gauze
-4x4 non-stick dressing
-4" kling/primed gauze
-2" roll gauze
-antibiotic ointment
-betadine/iodine
-rubbing alcohol
-steri-strips (assorted sizes)
-iodoform gauze (packing material) 1/4-1/2 is pretty multipurpose
-cotton tipped applicators
-disposable suture kit (get a couple with all metal tools and you can reuse the items) or purchase individual needle holder, pickups, hemostat, scissor, etc.
-assortment of suture material (2-0, 3-0, 4-0, 5-0 in absorbable)
-multi-shot stapler
-staple remover
-scalpel handle with handful of #11 blades or multiple disposable scalpels
-60cc irrigation syringes
-1" and 2" silk tape
-bandage scissors
-super glue or dermabond
-tincture of benzoin
Burns:
-Water-jel burn dressings for initial treatment
-Sterile irrigation fluids (either IV bags or bottled sterile water or saline)
-Non-stick dressings
-antibiotic ointment (do not use until tissue is cool)
-Silvadene cream
-narcotic pain meds
-NSAIDs (ibuprofen, naproxen, etc)
Anything beyond this level of care and the patient most likely not survive or wish they hadnt. Adding some surgical tools to deal with 3rd degree circumfrential burns is a consideration but requires a fair amount of knowledge to pull off and manage in the long term setting. In reality, what I listed in the “larger cuts” section could do it but I would want a few extras of each item at a minimum.
Fractures:
-4" compression wraps
-6" compression wraps
-full size SAM splints
-tuning fork
-traction splint (Hare, KTD)
-triangular bandages
-One step casting material
-Padded aluminum splints
-Pelvic sling
-Sealed pillows
-queen sized flat sheets
All of these are fairly minimal in design so as not to get too far above and beyond studying that could be done at home while still being fairly effective for moderate to severe injuries. With each of these you are going to need quite a bit of studying at a minimum but ideally some practice at least with a healthy patient or on models so you can get down some of the techniques where supplies are lost or wasted (bandaging, suturing, wrapping, splinting, etc).
As for treating larger wounds, it is more important to have the knowledge and discipline to not close a wound than it is to know how to suture someone up. Allowing a wound to heal by secondary intention is sometimes the best way to treat a wound although less glamorous than throwing a stitch in someone.
The quantity of this is going to be limited by budget, space, and expected duration of event. Most of this stuff is fairly inexpensive in the grand scheme but can take up a good bit of space. A single box of 4x4 gauze is roughly 5x5x4 and only holds 25 or 50 packets depending on packaging. Depending on the packaging you can vacuum pack some of this stuff to cut down on bulkiness but I would plan on at least a foot locker or two to contain these three kits.
Most of this stuff is available for purchase on the open market with exception to the silvadene (last I checked). Some additional items will help you to increase comfort and decrease mortality and morbidity in your patients include:
-assortment of NSAID and narcotic analgesia
-plain lidocaine for blocks
-assortment of antibiotics to allow you to treat common infections (skin, GI, EENT, etc)
This of course requires a physician to help you out and a firm commitment to maintaining a moderate to high level of knowledge. Just learning this stuff one weekend/week/month/year is not enough. It needs to be maintained.
In addition to the three injuries you brought up I would recommend planning on a lot of less dramatic but more probable events including: cough, colds, sniffles, fever, diarrhea, constipation, heartburn/gerd/ulcers, allergies, headache, sore backs, rolled ankles, ingrown toenails, fungal infections, tooth aches, blisters, debris in eyes, splinters, etc. These may not kill your colleagues but they will make them less effective in the day to day, not to mention miserable.
Most of this stuff could be treated with what you find in front of the counter at the walmart pharmacy instead of what is behind it.
Hope that helps,
ETA: Couple boxes of exam gloves and a box of sized sterile gloves, shouldnt have to mention it but to be thorough…