If we follow the 'anything imaginable' route then of course I'm simply going to pick game-breaking options, specifically:
1. A sniper rifle and plenty of ammo.
2. A machine gun and plenty of ammo.
3. An Army survival pack.
Thus I'm going to be more realistic and pick things from my own flat, which I can actually access within five minutes. I'd survive the apocalypse though, most likely, because within three miles of my flat is a TA base, where I could access weapons and ammo, and supplies. I merely need equipment to get me those three miles in the first place. Therefore, I would take:
1. My iPod Touch.
2. My laptop and its necessary peripherals (like the charging cable and such), inside its carry-case.
3. The BB gun my friend lent me to use as a film prop (he's using it as a prop for a play he wrote).
The BB gun is a proper replica, which is why we're using it in his play and the film I produced. We needed something that looked authentic (that isn't a real gun, as we're in the UK, it's a handgun, and we don't have gun licenses). So I can use it to trick and thus warn away people who try to hinder me while I escape to the TA base near me to get proper weapons and supplies. A decoy to prevent problems with fellow survivors, if you will. The iPod and laptop are basically for record-keeping, and for internet access and communication. My phone is always with me anyway which is why I didn't count it as one of the three above. When the internet goes down, eventually, then I can still use the laptop and iPod for keeping a log and record of events, and if necessary an information database. Good, accurate information is key to survival in any given situation, after all...