Our Big/Little system is slightly different from most chapters that I know of. Each of our new members get a different temporary big sis (or temp big) each week of their pledge period (6 weeks) and close to the time of their initiation they choose three people they could see as their big. Then on big/little night they find out which girl they actually received. I think this is such a great system because the new members get a big they feel comfortable with and have established a connection with instead of someone randomly deciding with whom they would be a good match. Also, girls can take littles as soon as they're initiated which works really well for us.
Concerning what LittleE said about not taking a little because you're graduating: yes, it is hard to develop a really strong bond in such a short time but if the connection is there then you'll continue the relationship even after you graduate. My big graduated the quarter after I was initiated but I really couldn't have seen anyone else as my big. She's the reason I joined Kappa Delta and we still have the best relationship and talk often! So it can work if you really want it to.