There are two broad areas to consider when dealing with readiness.
I hate trigger locks. They might satisfy the law but I feel they give a false sense of security. My opinion on where your guns should be: concealed on your person or locked in something bolted to the building.
* This is the condition called for at events when it is necessary for personnel to go downrange. In addition, handling of firearms is prohibited while anyone is downrange.
Not every firearm can meet these requirements simultaneously. For example, some have fixed magazines, or safeties that can't be engaged with the action open. At a minimum, remove the ammo, open the action, insert the chamber flag.
The answer to this question depends on many factors.
Guns that will be stored and not needed for some length of time should be unloaded. Nothing in the chamber and an empty magazine. Keep the ammunition someplace else. Ideally separate safes.
Most people assume that firearms are stored unloaded. Memory is not as good as we would like it to be. I can't remember to water the plants, let alone try to remember which gun might have been stored loaded. The last thing you want is to have an accident because you "remembered", or somebody else assumed, that the deer rifle you put away at the end of last season was unloaded, when in fact it wasn't.
Store them unloaded, and check anyway when you get them out again!
When you keep a firearm for defense, the tradeoff you face is safety vs availability. Unfortunately maximum readiness is at odds with maximum safety.
An unloaded firearm locked in a hidden safe is not likely to be involved in an accident, but it is also not readily available for defense. On the other hand, a semi-auto, cocked, with the safety on, sitting on your nightstand, is an accident waiting to happen.
A good compromise is a quick access lock box that is out of sight but accessible. Loaded magazines or speed-loaders can be kept in the box as well.
Do not underestimate the persistence and resourcefulness of children. How successful were your parents in keeping their "contraband" out of your hands? Your kids are probably no different. Get a box that is reasonably tamper-proof. Teach your kids age appropriate gun lessons so that they will grow up to be responsible gun owners.
I'm a big fan of concealed carry. Forty-nine states have some path to legal concealed carry. Illinois and DC do not. In some you need no permit. Others require a permit to carry concealed, but not to open-carry. Many require a permit for any kind of carry. Know the law in your area.
The big debate among my friends and associates is whether to carry with one "up the pipe" or not. We are talking about semi-autos. "Up the pipe" means a round in the chamber.
A revolver has a cylinder which is basically a revolving chamber. If it is loaded you have a round ready to fire, just like a semi-auto with one up the pipe.*
A double action typically has a long hard trigger pull. It is difficult, but not impossible, to fire one by accident.
I have read recently of three cases of unintended discharge. In one case the drawstring on the waist of a jacket caught the trigger as the gun was holstered, shooting the gun owner in the calf. In another case a crease in the holster pulled the trigger as a man got in his car, shooting him in the thigh. In the third a woman was fatally shot when she grabbed an off-duty police officer around the waist at a party.
Carrying without a round in the chamber prevents accidents like these, but adds the step of working the slide in order to meet a threat. In most cases it is worth the added margin of safety to carry with an empty chamber. Practice working the slide with dummy ammunition. Don't forget to learn some one-handed techniques.
A single action may or may not be safe to carry with a round in the chamber and the hammer down. On the one hand they can't be fired from the hammer down state by pulling the trigger, on the other hand some will fire if the hammer is jarred or pulled part way back and released. Many modern single actions have mechanisms to prevent this. Read the manual. Know your gun. Remember mechanisms can fail.
A second issue with regard to carrying a single action semi-auto with a round in the chamber, is how to get the hammer down safely. When the slide is worked to chamber a round, the hammer ends up cocked. On a 1911, and many others, the hammer has to be controlled while the trigger is pulled in order to lower the hammer without firing the pistol. Obviously there is potential for an unintended discharge in this situation. Some pistols have a de-cocking mechanism. This is better, but mechanisms can fail. To carry out this operation you must have a safe area to point the muzzle in case of an unintended discharge.
Carrying with a round in the chamber and the firearm cocked with the safety on, often referred to as "cocked and locked" or "condition one" can be dangerous. The energy to fire the pistol is now stored in the main spring. If the safety is inadvertently disengaged the pistol can be fired very easily. Many pistols have passive safety devices to prevent this, like the grip safety on a Colt 1911, but mechanisms can fail. That said, many people do carry cocked and locked and there are some good holsters designed to make this safer.
As for me, cocked and locked is only for situations where there is a high probability of a gunfight occurring in the next twenty seconds. If I have more than twenty seconds, I'm going to get the hell out of Dodge.
Keep your gun in the safest state consistent with a realistic expectation of needing it.
* You could carefully position an empty chamber such that the empty one
will rotate into the firing position if the revolver is cocked or the
trigger is pulled, but to me this system seems prone to failure and in any event it will fire on the next trigger pull.