Clothing:
Leather gloves with surgical gloves underneath them (my parents own a veterinary practice)
A long sleeved rain-jacket with a hood over a long sleeve shirt.
A cycling helmet over the hood with goggles and an improvised gas mask made from medical equipment (paper mask filter, surgery glasses, plastic, cloth).
Long cargo pants (many pockets, hard to rip) covered in plastic to try and minimize risk of infection.
Takkies and long socks with Wellington boots on the outside.
The joints between the boots / legs and gloves / jacket would be duct-taped down.
Weaponry:
I would take a light aluminium pool cleaning staff, and replace the head with a massive meat knife. It would be short enough to carry but still have a good range and could be use as a walking/ climbing stick. I would get a whetstone to sharpen it.
My father's pistol and its full safe of ammo would be coming with me (small safe, not too much ammo to carry

)
Gear:
I would carry a length of plastic rope, very light, very strong, can be used for many many problems.
A small backpack for vitamin tablets, dry snacks and water would be essential. Also used to carry the rope, a lighter, a knife, some basic medication (painkillers, anti-septic, antihistamine, and an adrenaline booster or two in case of REALLY REALLY bad shite. All this would be available in the veterinary clinic. A small net for catching pigeons and food animals would be useful too. A wind-up torch for night time expeditions.
Hopefulness:
If I got really lucky and found a flame-thrower or managed to improvise with lighters, an old telescope tube and wire, petrol everywhere would come in handy and allow me to actively attack slightly larger hordes if necessary.
Plan:
Get the hell out of the once dense city, preferably with company who are both trusted and well armed. Go into the deeper country where there were fewer people and fewer zombies waiting to happen. If I had to hole up, it would be somewhere high, in a sturdy building with only one stairwell and a concrete roof.