How old? Boy or girl? name? MORE DETAILS please!!!
Food and water bowls (we use Foster's and Smith's long-eared water bowls - they're narrow and deep so the ears fall to either side but not IN the bowl), a leash, a collar, a harness for walking, a dog-bed (on the off-chance that you can get him or her to actually use it instead of your bed or couch), a Kong, a squeeky ball (Moe's favorite cost a buck at Job Lot), nail trimmers, Milk Bones, Greenies, any good quality dog-food that your new friend likes (we use Iams and sometimes Purina Pro Plan - your vet can suggest something for you), ear cleaner, cotton pads to use with the cleaner, dog shampoo (something mild that deodorizes - don't bathe too often because it increases the hound-dog smell), a dog brush or a shedding blade (I prefer the blade), and maybe a clicker if you want to try clicker training (search for "Click and treat" on the web - it's so easy that a child can do it and it works). There are optional things like doggie doors, dog life-vests, bandanas and other articles of doggie clothing, carpeted steps and ramps to help him/her get onto furniture or into cars,
and eventually you may even get another Basset to keep him/her company. :wink:
Obviously you don't need everything all at once but I assure you, you WILL own all these things and more evnetually. 8)
Good luck to you and your new friend - here's wishing you many years of happiness together!
Terry