You don’t have to have a state of the art medical bag. Start off with the basics. Pick up some band aids and cold packs to start off with. Gauze pads are pretty easy to find and would come in handy if you have to cover a wound or stop some bleeding. Add Medical tape to secure any gauze that you may have to apply.
Tourniquets should be in everyone’s kit. Be sure not to skimp on purchasing tourniquets. I recommend North American Rescue products.
Israeli Bandages are another common item in first aid kits. These take a little education to be used properly.
After a little training Israeli Bandages can come in handy for various scenarios.
The Red Cross has more info on what you should do in an emergency.
I have gone through some military first aid training and have taken CPR classes in the past. Check in your local area for additional training. CPR/ Basic First aid is training everyone should go through.
What does your kit look like and what training do you have?