Arming myself would be difficult... The closest thing to a bat would be one of my golf clubs, but they have carbon fibre shafts and are probably not very effective. A big knife out of the kitchen would probably have to do for the moment.
(That reminds me that I should have bow&arrows and some decent bat-like objects in the cellar, but going down there would probably be suicide with zombies around.)
Escaping my flat/apartment would be even more difficult. 4th floor is rather high. Either one of the two stairways would have to be zombie-free or i'd be brave enough to take the elevator. (hoping that there are no zombies waiting at the ground floor)
The last option would be to jump for a tree. It's only 2-3 meters from the balcony, so it might work.
When I'm finally on the street, I would try to get to my car (hope I'll remember where i left it
).
Next destination would be a police station to find some guns.
Aferwards I'd drive to the nearest Land Rover dealer and get myself a Land Rover Defender. Probably more useful than a new mini when u have to run over zombies and the going gets rough. (I don't actually know a Land Rover dealer....damn)
Next stop would be at a petrol station for lots and lots of diesel, some good maps and some snacks
But what to do then? I'd probably head for the countryside, hoping that there are less zombies there. Probably find a military base and get myself an assault rifle and hand grenades and other decent equipment u won't find at a police station. (I've actually got no idea where the next military base is)
But what then? U should be able to get food from super markets for a few years, acquiring fuel for the car wouldn't be such a big deal either, but finding a save place to sleep would probably be.
I'd say your screwed anyway if you are alone...
looking for other survivors would be priority number one.