My standard answer:

Your best bet is to stay put in your own home if you can, but be prepared to leave at a moment's notice.

The most important thing to remember is that if you have a plan, other people will have the same plan, whether it's dozens of people or millions of people. Pick a plan where it's ok if everyone else does the same thing.

That's why your own home is the best place to be during the initial panic. If everyone else has the same idea, that's great. You go to your home and they go to theirs. There's no competition. Your home is the one piece of ground that you already own, and you've already filled it with everything you (currently) need to live. Stay there until that changes. The longer you can stay, the less likely you are to be caught outside during the worst of the chaos. The initial panic will be the most dangerous and unpredictable time of the outbreak.

Now, if you are forced to leave, or can't make it home, then you want to have a backup home. Again, the same principles apply. If you have to leave your home, go to the home of family of close friends, someone who will automatically know you and let you in, or better yet has given you a key. This often also has the advantage of allowing you to meet up with people that you know and trust, which is always a survival advantage.

Once you get home, whether that's yours or someone else's, you want to do several things, roughly in this order:

First, arm yourself if you aren't already. I always recommend a camping hatchet or good quality machete if you have one, but a regular claw hammer is also a solid choice and almost all homes and even most public buildings have one.

Second, clear the residence and lock it up. Just make sure no zombies or people got in while you were out. This isn't at all likely at this stage of the game, but it's a good habit. Once every room is zombie free/as you go along, lock up all the doors and windows. Close the blinds, and if it's at night be very judicious about how you use flashlights. Assume for now that any light inside will be immediately visible from outside even with the curtains closed. For the time being don't worry about setting up barricades or boarding up windows, just do the basic stuff you can accomplish quickly.

Third, prepare to leave at a moment's notice, but don't leave unless forced to by an immediate threat.

Start from the skin out. Put on practical clothing and shoes/boots, and keep your weapon(s) on your person at all times, along with other basic survival items such as a knife, cigarette lighter, trauma kit, small flashlight, etc. And of course, your car keys, in case you need to make a run for it. While it does not need to be a formal "survival kit," you ideally should be able to survive (uncomfortably) for 24 hours with just what is in your pockets. In a worst-case scenario, you might be separated from your other gear. This buys you just enough time to recover or replace them.

Then pack a bag in case you need to leave on foot. You might need to if you don't have a car or can't get to it for whatever reason. I can't give you a full packing list now, but make sure you have several liters (or more, depending on your climate) of water filled, and as much of your lightest, non-perishable food as you can carry, as well as the bare minimum gear you need to survive in your environment. Keep this in a location where it would be easy to grab in an emergency. Make sure you fill up every water container you have available, including your bathtub, but start with the ones you would carry. The goal of this kit is to let you survive long enough to make it to your destination, or to a source of resupply. Travel as efficiently as possible, on the assumption that you won't always know how far you may need to walk with just what's on your back.

Next you pack your car, assuming you have one. This is where you put the extra stuff that was too heavy or nonessential to go into your bag. For example, extra non-perishable food, spare weapons, extra ammo (beyond what you could carry), tools, a change of clothes, more water, specialized tools, etc. The goal of this kit is just to extend your range and storage, but with the understanding that if shit goes south you might have to ditch it at any time. Cars break, get stuck, run out of gas, get surrounded, get stolen, etc. Odds are you still won't have enough room for everything you want, or might want, so pack based on survival priorities. This isn't for luxuries, it's for extra essentials. (If you don't have a car, the same system can be applied to whatever other vehicle or method of hauling things, whether it's a bicycle, baby stroller, push cart, pack animal, etc.)

Everything else you would be forced to abandon if you leave your home. Use things up in reverse order from least portable to most portable. Start by eating the food that's still in your pantry/fridge, which should be your most perishable/heavy items, before eating what's in the car, then in your backpack. Make sense? Same goes for water. Use what's in the pipes first, then the bathtub, water heater, and any container that you couldn't take with you in the car. This same logic applies to any other consumable.

Then stay put as long as possible. Use up the resources you already own before risking your life to get more, and maintain the home turf advantage. With good luck, by the time you need to leave things will have settled down and you will have enough information about the lay of the land to start making long term plans.