I have a first aid kit that goes with me to all my dog sport events, camping, in the car when we go on trail hikes, etc.
For first aid/wound care it has:
Saline wash (I prefer this to peroxide to wash wounds as it is gentler to the tissue)
Isopropryl Alchohol
Betadine liquid (my preferred antiseptic)
Styptic powder (to stop bleeding)
eye wash solution
Cotton balls
Q-tips
non-stick gauze pads in assorted sizes
a couple of rolls of cotton wrap
a couple of rolls of Vet Wrap or similar self-adhesive wrap
scissors
sports tape
Other stuff:
nail clippers--to trim torn nails
tweezers--to remove ticks we pick up on the trails
a couple of pairs of latex gloves
dog aspirin
benedryl
grooming wipes--for quick clean up of muddy paws
sample sizes of my dogs' food in case we're out longer than expected
extra dosage of my dog's medication for the same reason
a couple of bottles of water--to drink or to splash on the belly/groin of an overheated dog
a couple pouches of GoDog electrolyte powder in case of diarrhea or dehydration
an ice pack--because I've been known to injure myself too
some band-aids--again for me
a roll of poop bags
I keep it all in a pretty decent-sized tool box. Inside the top cover I taped an index card with my vet's number and address, area emergency vets' numbers and addresses, and the number for the animal poison hotline.