Well, if you are flying to NYC just to see RENT, you should buy tix in advance - they have codes for $45 front mezz. tickets.. I never did the RENT rush, so i can't tell you about that, sorry
It's all about chance. Saturday might be packed or completely empty. Don't count on it being empty and that's your safest bet. They don't do rush at the Neder, but lotto. About 2.5 hours before the show starts (about 5:30), you put your name down on a card and whether you want 1 or 2 tickets. If you win, the seats are 20 bucks each and are in the first two rows in the orchestra. You need your ID with you if you win. Make sure you bring a discount code with you in case you lose lotto that way you don't have to pay full price. They don't usually allow for the student discount on Saturdays I don't think, but there are other codes out there. It's much easier on the wallet that way. Rent discounts
I met some people who did lotto Sunday matinee along with me last weekend and we got talking...they had lost the lotto on Saturday matinee AND evening...they said Saturday night was INSANELY busy...100-150 people at least for the Sat 8pm lotto...my advice is if you want to go Saturday night...buy tix in advance...
I would recommend Sunday if you can swing it...most of the tourist crowd is on their way out of town...
If you are set on going on Saturday, wait til after New Years and go in Jan or Feb