There are many things to remember when your combing the wastelands of a future suburbia. Mind the zombies, don't anger the mutants and remember to have a melee option. However, there are actually quite a few “real” things people would need to worry about should they want to/or have a game master who likes a little realism in their world gone to hell game.
1. Don't burn the sofa. If you need to make a fire (especially for food) don't ever use worked wood. Most woods that have been used in home construction, furniture and Cabinet making and so on have been chemically treated to last longer, stained or some combination of the two. When burned this wood releases the chemicals and can cause any number of problems. Including insanity.
2. Get a bike. Gas and electric power are going to be hard to get a hold of after a little bit of time and sooner or later it will run out all together. Breeding, caring for and feeding a horse can be difficult and you cannot run them into the ground. Bikes, however, are small, little, quick and require nothing more than a set of legs to make them move. In the long run they aren't as fast as horses and will eventually break, but taking good care of one, and learning a little about the repair of a bike will be a grand help to you and your party.
3.When it rains. Screw the concept of “acid rain”, yes rain water can corrode and is no pH balanced, however, it is a lot cleaner and a lot better for you than almost any river, stream or lake will be for quite sometime after things go bad. Most waterways in the US are connected to sewer treatment plants. Once those stop working (which will be relatively fast) all the unprocessed human waste will be dumped into whatever may have been a halfway decent water source.
4. The root of salary. Salt, sugar, coffee, chocolate … if you get your hands on even a little of this you are rich. Oh yeah, people will be trying to get money, things and food … at first but after awhile these creature comforts will be in high demand, and worth a good price (just don't pay for it in bottle caps!). Remember throughout human history wars have been fought and people have died for these things.
5. Get a Nurse. Listen, nurses do 95% of the work that doctors get credit for. It is the nurse that sets and casts the broken bone, the nurse that stitches the wound and he nurse that assesses and typically tells the doctor what is wrong with the patient. Unless a member of the party needs open heart surgery or an appendix removed get a nurse (an RN is better but an LPN is just fine).
Other things to remember:
Electric power may or may not be a normally available commodity. And if someone can get it than chances are they had money, power and enough of something to keep their place of electric power running. Don't go running after these guys anytime soon.
Food from stores, supply rooms, etc will eventually run out and depending on how well previously established supply channels are working may never be restored. Also remember that once gas runs out farmers will have to return to older ways of planting and harvesting which means there will be less new supply. One last thing to remember with food: After the house pets are eaten the next slowest and easily caught meat is a human.