How big? IMO, as big as it takes to carry the stuff you will realistically need to treat the type of injuries you are most likely to suffer while pursuing whatever activity you're doing.
Heading out in about 20 minutes when the traffic clears.
Here is what I carry for dayhikes and overnighters at the moment.
1qt freezer bag w/:
a few sterile pads and bandaids
2 individual use Neosporin packs
2 ACE bandages
1 roll athletic tape
couple of anti-diarrheal tabs
muscle relaxers and painkillers in a little medicine tube
Since I've got a knee and ankle that give me trouble sometimes, and will be hiking some steep trails, I add:
ACE ankle support
ACE knee support
Got rubbed raw working an extra shift where I stayed soaked in sweat, so added a tube of anti-chafing gel I'd been wanting to try.
Without these extras, only the bottom half of the bag is full, so it doesn't take up much space.
Mostly care about the athletic tape and ACE bandages, as a sprained ankle is at the top of my list of possibles on rocky terrain. I'm not likely to need the sterile pads for anything, but they don't weigh anything, either. Besides, if I'm most likely to tear up an ankle, it's probably going to be taking a fall on whatever rocks are available, and maybe getting scraped or cut up in the process.
The first aid kit with my climbing gear has mostly the same stuff in a zippered bag, with the addition of a heavier duty elastic bandage and a pack of QuickClot.