Kitchen burns could require burn creams, gauze pads, and tape or freeze packs. Cuts and scrapes require antiseptics and bandages. Body aches and sore muscles could require analgesics or heat-generating creams. Look for an emergency kit that contains the largest variety of healthcare items. The emergency kit may have to be portable enough for a first responder to take to the victim. Look for first aid kits designed to be carried like luggage if you think you may need to bring it to the accident scene. 
If you anticipate the patients will come to the kit, you may want to invest in a wall-mountable metal emergency kit. A suitable place to mount such a kit might be in the bathroom near a sink or a wall in the kitchen out of the line of traffic. If the kit contains medications or other dangerous chemicals, you may want to mount it out of the reach of children. They can have a smaller kit of their own filled with bandages and other harmless items.
Another element to consider is expansion. Can other items be added to the basic emergency kit as the need arises? Some homeowners may need to add glucose tablets for diabetics or blood pressure monitors for those with hypertension. There are even home versions of cardiac defibrillators and CPR breathing masks available. Check to see if the manufacturers of an emergency kit also make additional items or refills. Emergency kits have ingredients which need to be replaced periodically, so make sure you can purchase these items independently.
Overall, a good emergency kit should contain enough medicine and medical supplies to handle everyday household emergencies from burns to cuts to accidental poisonings. It should allow you to make the victim stable enough for medical professionals to take over treatment.