Forget a bed! They will colonize yours or your sofa!
Seriously, get a big one - they stretch out for miles.
When you adopt, a REPUTABLE charity will advise you on what you will need. Main differences from other dogs are the lead, collar and coat.
Greys have no body fat and thin fur so it's normal for them to wear a coat when out on walks - most of them hate the rain too. Many owners also get a fleece indoor coat for cold winter nights, especially if house is cold/draughty/old. Most charities will sell you these items - it's a useful fund raiser for them. Also because of their shape, a normal dog coat won't fit them. Have a look at them on the net, you'll see lots of different types.
Collar - any sighthound has a thin long neck so they should NEVER wear a normal dog collar as they can reverse out of them very easily. Either get a leather greyhound collar or one of the increasingly popular martingale collars. You'll need a lead with a strong clip, not one of those extending ones, they are dangerous and should never be used with greyhounds.
Bowl - any bowl - we use metal ones as they are easy to clean. We raise bowls - use Ikea flower pots as they are the perfect height, but some people feed off the floor or you can get special dog bowl holders.
Please be guided by the charity when deciding on your dog. They will know the dog's personality and history and this is more important than you liking the "look" of a particular dog. Of course it's natural to express preferences e.g. cat friendly but they will be able to match you properly. If the charity simply lets you walk in and pick one based solely on looks then walk away as they are not behaving responsibly.
Also, depending on how old your DC are, please ensure your DC are able to understand that greys are generally quiet dogs that spend a lot of time sleeping - they are not like JRT or similar that are into everything and superbouncy - quite the reverse. You'll get the occasional mad five minutes then it will be back to the sofa for a powernap. Some greys would find a noisy house with lots of kids quite stressful - make sure the dog has somewhere quiet they can go where kids won't disturb them, and that kids understand that greys often sleep with their eyes open so need to learn about not bothering them.