You may have misconceptions about how well a greyhound would work as a household pet. The dog was bred to be a hunting dog, with features that are slick and aerodynamic in order to offer speed, and independence that results from chasing animals without any sort of human interaction. This breeding has resulted in personality quirks for the breed, which include the natural drive to chase. The other animals in you area will be tormented by the greyhound if it allowed out without a leash.
This breed of dog will also instinctively fight being confined. Their need to chase will lead to the dog giving chase to anything that moves very quickly. This includes animals, running kids, anything. The best safeguard is to always use a leash. Training will not remove genetic behavior. Despite all of this hunting instinct, the greyhound is surprising in its laziness. They are pretty submissive and calm, and quite the lounger. They will have loving personalities and are capable of following commands pretty well, unless they are in the mind to chase something.
This surprising behavior is a result of breeding for rapid releases of energy. They are meant to spot, give chase and subdue a target in mere minutes. Greyhounds spend most of the day living like a cheetah, sleeping and saving up energy for when it needs to release it. This does require the owner to be prepared to give the greyhound exercise if its living conditions do not give it such an opportunity. The breed can live in a small apartment or other small confines, but they need space to exercise. The canine will have periods of extreme energy and will release it either on your terms or on his or her own terms.
Just about every greyhound that can be adopted are retired racers. They are trained for routine. If you use outside time for exercise, they may also use the time for bathroom needs as well. Overall, the breed will offer a loving personality and demeanor, and they will lay around the home most of the time. When it is time to go out, at the exact time the are used to going out, they will perk up and be prepared to exercise and take care of business. As an owner, you just have to be willing to follow the routine. What it comes down to is if you are willing to work with an animal that will follow your lead most of the time, while it is not in a single minded state to chase its prey. Keeping this in mind will prepare you for all of the possible difficulties in the breed.