Everything these folks have said!
I will say that scared feeling will go away... don't let go of the leash, but as you form a bond with your hound, and they settle in, you won't feel like you need a death grip on them.
They will stay with you.
We have always had our greys on leashes outside of our yard, and will continue to do so. You many critters and cars around.
On another note, if you do adopt a grey, you are gonna fall in love!
Good luck!