I have thought this out a lot
Assuming the zombies would be similar to those of the walking dead or 28 days later, the first order of business for me would be to get the heck out of the city. I live near the edge of wilderness, so it wouldn't take me too long to start getting into thicker bush. If it was beginning in my city (the infection or what have you), I would try and give myself no more than maybe 30-60 minutes to pack a hiking backpack and get moving.
Some people want to take their chances boarding themselves up in their houses until the chaos is over (I am a regular on a walking dead message board so we talk about this a lot lol) but I think that would be poor strategy. First of all, what if zombies end up hanging around your neighbourhood? If you live in an urban area there would be a good chance, imo, that they would hang around for a while after the initial massacre in the hopes of finding scraps and people missed in the initial wave. Also, I don't like the idea of being stuck holed up somewhere in the hopes that something will move on, while watching your rations slowly dwindle. No, the best strategy is to get as far away as possible from civilization.
If you make it that far and are out of the immediate danger zone, the next plan of action would be to look for a secure area to build camp. I have toyed with the idea of trying to get my hands on a boat of some sort and anchoring myself in the middle of a lake with a dinghy for supply trips, and I like the idea except it would be unrealistic to hope to live out there for any length of time due to inadequate resources. If I can find a safe place that would be easy to secure next to a lake or water body, I would probably anchor the boat out a ways and use the dinghy to travel there to sleep at night. That way I could probably sleep much more peacefully.
As for the secure area, I would want to have the space to possibly keep some chickens, grow some food, store supplies, etc. If I could scavenge one from an abandoned farm or whatever, a horse would be useful to keep for travelling purposes as well.
Whenever possible, I would fish for food in the lake. Obviously this could probably not be relied upon, so I would hope that although I want to be somewhere rural, I would also be within accessing distance of a low key area I could scavenge a bit from.
What I would like to do is assemble a pack with supplies and learn how to use weapons. I am actually going to be learning how to use some weapons this year
As for the pack, it is a work in progress. I know roughly what I want in it, but have not assembled it yet. It is going to include as much of this stuff as I can fit in or carry easily:
1. First Aid Supplies + toothbrush.
2. Some non-perishable food that could get me through a couple days until I found a place I could scavenge.
3. Water bottle (full) and water purifyer.
4. Basic fishing gear, hunting knife, and fire starter.
5. Rope.
6. A bit of extra clothing.
7. Tiny sewing kit.
8. Pen/pencil and notepad.
9. Survival guide (I actually consider myself somewhat knowledgeable but never hurts to have a small pocket sized one around).
10. Small pot for cooking.
11. A tiny bottle of supplements - you just never know what you will be eating or not eating...
I know I have more but they are escaping me. If I think of them I will add them
Although this is with the zombie apocalypse in mind, a pack like this would be a great thing to be able to grab quickly in emergencies so... Call me crazy but it could be useful!