Feeding

Food (We're big fans of Hill's Science Diet)
Training treats
Nutritional supplement (To stimulate the appetite of picky eaters)
Bowls
Placemat
Food storage
Freeze dried kibble enhancers
 

Walking

Harness - soft step-in style
Training collar
Training Leash (We do NOT recommend retractable leashes!)
Waste bags and dispenser for leash
Treat dispenser bag
 

Play

Inedible chew bones
Stuffing-free plush toys
Toy box or litter box - to use for toy storage
Playpen
 

Sleep

Basic Crate
Crate pad
Crate cover (you could also just use a sheet)
Bed

Training and Clean-up

Housebreaking bells
Stain and odor remover
Chewing deterrent spray

Travel

Car seat
Travel bag
Doggie seatbelt
Travel bowls
Car seat protectors
 

Grooming

Shampoo
Brush
Comb
Eye wipes
Toothbrush/paste
Nail grinder or trimmer

Misc

Identification tags
Life jacket
First Aid Kit