Start with some basic first aid kits and expand them over time (Tony’s First Aid Kit). For my home and vehicle kits I purchased complete kits and then repackaged them into 2-sided parts totes. This allows me to easily see and access items. Get a smaller kit for a hiking pack. Have duplicate supplies in your home kit.

This is the most important component because you will use this even in non-emergencies. This is a minimal list of first aid essentials. Add other items depending on your specific requirements. Basic first aid supplies should include (in alphabetical order):

Alcohol Pads for cleaning wounds, cleaning equipment, and starting a fire.
Antibacterial cream for cuts, scrapes, and wounds (bacitracin, polysporin, etc.).
Antihistamine to treat allergic reactions such as insect bites.
Antiseptic wipes for cleaning wounds.
Bandages: Assorted adhesive bandages (fabric preferred) and wraps.
Closure Bandages such as butterfly bandages or Steri Strips to close larger wounds.
Disposable Razor to shave around wounds to make bandages or Steri Strips more effective.
Gauze Pads: Sterile gauze pads (various sizes).
Hand Sanitizer can be used for hygiene and for starting fires.
Insect Treatment to reduce the effects of insect bites.
Manual with first aid directions.
Medical Tape for larger wounds.
Moleskin or other blister treatment.
Multi-Tool (small) with tweezers and scissors (Leatherman Micra)
Pain-relief/Anti-inflammatory medication: Ibuprofen, aspirin.
Panty Hose can be used to make a tourniquet, as a water pre-filter, for warmth, and protection against parasites (yes, it sounds weird but read the article).
Safety Pins are useful for a variety of tasks.
Snake Bite Kit to reduce the effects of snake and insect bites.
Steri Strips are long, thin, adhesive strips for closing wounds. Protect closed wounds with a protective dressing. Can also use butterfly bandages.
Stomach Pills such as Pepto Bismol, Alka-Seltzer, etc.
Super Glue in small or single-use tubes for repairs and for closing wounds.
Tape Card (duct/electrical tape): backup tape for large wounds, splints, etc.
Zipties can be used for repairs, splints, etc.
Water Filter Syringe can be used for flushing wounds (see “Other Uses”).

Add additional items depending on conditions and requirements. Here are some good items to add to your kit:

Clotting Agent can stop bleeding quickly (this stuff is pretty amazing). It is available in a variety of form factors including packaged powders, clothes, etc.
Extra Bandages (cloth bandages preferred) with strong adhesive since these are normally the most used items in the kit.
Extra Alcohol Pads: can be used for first aid and for cleaning equipment.
After Bite medication to soothe bug bites.

Start with a basic kit and add items as needed. Be sure to rotate supplies such as medications that can expire. Occasionally check items such as alcohol swabs that can dry out over time. Be sure to include ample numbers of each item. I started with a basic Cabela’s Waterproof First Aid Kit and expanded it to better suit my needs (details).