Water. When the zombie apocalypse happens, there are high chances that clean water won't be easily accessible. Even if you run out of food, your body will use the reserves, such as sugars, fats and eventually muscles, which will keep you alive for a while (depending on various factors, e.g. physical condition, percentage of fat, age, diseases etc).
Then, take everything canned you can find. Canned food can last for a couple of years, especially meats.
Get some sugar and some salt. If you get an infection, leading to the loss of water (vomit/diarrhoea), you can make an Oral Rehydration Solution.
Get some strong alcohol, like cheap vodka and brandy. You can use it treat wounds, as well as to make fire (which increases your chances even more). It also can be used as a disinfectant for food and surfaces.