Most first aid kits are boo-boo kits, stocked with band-aids, gauze and antiseptic ointment. Not that there's anything wrong with that, until you're staring at a severed artery, gushing cavity or sucking chest wound. Then you need a trauma kit, and unlike a boo-boo kit trauma care can't wait until you get home. Trauma kits require training, so use the google and find something like the Wilderness First Aid and Wilderness First Responder courses from NOLS.
Condor's Rip-Away EMT pouch is big enough to carry the things you need: a tourniquet, combat bandage, clotting gauze, shears and chest seals. For a good rundown of the individual components, check this out this link. This pouch has plenty of organization options to set up the contents any way you please. There are internal and external keeper webbing points, MOLLE webbing and small rip-and-stick panels for morale patches.
Condor's pouch has one more feature, and it's a big deal: the pouch is attached to a stiff, flat fabric panel covered with a large rip-and-stick patch. The panel has straps to mount it to a headrest or other surface, and then you just press the pouch itself firmly against the rip-and-stick patch to secure it. When you need it, just grab the handle, give it a firm yank and run like hell towards the blood. There are two dimensions to this vital increase in speed: first, the ability to grab and go, and second – and maybe even more important – is that you always know exactly where the kit is. When time is tight and lives are on the line, be prepared.