On the list of items that missionaries are to bring with them is: First Aid Kit. There are a LOT of first aid kits out there don'cha know! (said in my very best Minnesotan accent...my husband served his mission there) They all contain LOTS of stuff and LOTS of stuff that missionary's probably would end up bringing back home with them. Our first missionary took one of those. For our second missionary, I decided to put one together myself. All you have to keep in mind is this: What might my child need at the spur of the moment when he can't just run to the medicine cabinet or drug store. Probably not a triangular bandage or a mouth guard. Maybe, but probably not.
I picked up a sturdy plastic box from the office supply store for less than $5. I liked how it had plastic 'bits' on the bottom part of the box that snapped over the lid keeping everything securely in place. I was worried that if it was just a snap on lid that it might just snap off during transit. Not a good thing. Everything needs to be neat and tidy. THAT is a good thing. It was about 6"W x 4"D x 3.5"H...Just make sure that your tallest item will stand up. It will probably take up less room standing up then laying down...at least I do.
There are a plethora of first aid items that the "List" says to bring with them. I won't list them here because they are different for each mission. Refer to your list and use your own discretion when deciding what size to purchase and what brand to bring with you. For example: Ibuprofen is Ibuprofen even if it is the store brand however all cough syrups are not created equal. Use what you already know works for your child. Don't send the industrial size Tylenol from Costco if you don't remember the last time your child even took Tylenol. Small is better. You can always send more or they can pick up more in the mission field. No need to include a box full of band-aids...wrap an elastic around the outside of the band-aids and discard the box, do the same with disinfectant wipes, etc. Only include the box if there is pertinent medical instructions that are only listed on the outside of the box.