I second Aldi, and check your weekend newspaper for coupons. When we moved into our apartment 3 years ago, here was the list I emailed to my husband for our first Home Depot and grocery store run - it's a mix of pantry and not, but I removed all the produce from the list. Note that this is VERY dependent on what kind of cuisine you make.
coffee filters
garbage bags
hand soap
can opener
ice cube trays
toilet paper
paper towels
flash light
all purpose cleaner
dish soap/dishwasher soap
mop/bucket
sponges
broom
dustpan
plunger
toilet brush
doormat
salt
pepper
spices (old bay, bay leaves, oregano, thyme, rosemary, paprika, chili powder, cumin, cinnamon, garlic powder, onion salt)
canola oil
olive oil
red wine vinegar
whole wheat pasta, spaghetti and shells
2 jars pasta
bag of lentils
bag of chick peas
bag of black beans
bag of white beans
sun dried tomatoes
jar of olives
2 cans tuna
Dukes Mayo
yellow mustard
Dijon Mustard
ketchup
peanut butter
jam
Bisquick
coffee
apple sauce
raisins
walnuts
honey roasted peanuts
brown rice
vanilla extract
oats
cornmeal
all purpose flour
baking soda
baking powder
1 large can diced tomatoes
Tabasco
Worcestershire sauce
soy sauce
bouillon cubes (chicken & beef)
honey
maple syrup
salsa
brown sugar
white sugar
I'd add potatoes, onions, garlic, cold cereal, crackers, tortilla chips, tortillas, bread, frozen veggies and meat, and basic produce depending on what you like (bagged salad, apples, carrots, lemons, etc.).