How important is pot size?

[let_it_grow]

I have a NOID that i got from a really shifty convenience store, I didnt think she was gonna make it... her leaves were tattered at the ends, the pbs were shriveled and some had no leaves on them and she was potted in a poor quality potting soil :O. After repotting and some TLC my poor little girl pulled through. She has a couple pathetic looking pb that she grew while regaining some roots (they were almost all rotten) and is now in the process of growing (what looks like its going to be) a nice big healthy pb. My question is... How important is pot size? Her pbs grew in a straight line rather than a cluster so i need a big pot to fit her lengthwise. Can i cut off the old pbs that have no leaves on them? Do they provide nutrients to the other pbs?