A fenced yard, or if you live in an apartment, they may want to see in writing that you have permission from the landlord. Quite often a rescue contact will even make a house call to see that you really do have what you say you have. They are not singling you out. They will want to know if you have children, their ages and in general about your life and your routine. For your part, you need to let your rescue contact know what you are looking for.
Age ranges, sex, personality, training health etc.
Give your contact as much information as you can and be prepared to receive a little education along the way. One other thing is to be a little flexible with those things you can be. I can't stress this point enough. Most dogs that come to rescue are between a year and seven years, not having hard facts I would guess that many are in the one and a half to three year range and maybe more males than females. I do feel comfortable saying that probably half or more are pet store dogs.