So this falls under the "toy" category, but Kongs are your best friend, especially for alone training or leaving for a short/long amount of time: http://www.kongcompany.com/. Fill it with treats, peanut butter or yogurt, and the greyhound will be distracted and then potentially exhausted.

Also, bitter apple spray is your friend for defending anything -- furniture, linens, etc. -- from potential teethmarks. http://www.amazon.com/Grannicks-Bitter-Apple-Bottle-Ounces/dp/B00028ZMEO. I use it a lot to deter them from my bookcases. If that doesn't work for some reason, talcum powder (i.e. baby powder) might work as well.

A brush can also be good, despite their short hair. I got one just for using every few months or so, but you can wait to get that for down the line. I got this one for the greyhound: http://www.petco.com/product/100491/KONG-Zoom-Groom-Brush.aspx