sorority recruitment

Rushing as a sophomore puts you at a slight disadvantage but it's definitely possible, and you'll probably have a lot of options if you're a well rounded PNM.
Everything depends on you, regardless of whatever grade you're in. If you have a high GPA, if you're very involved, and if you're wealthy and pretty then you'll have a really good amount of options. However, if you're an average girl with average grades/looks/etc. then your options will limited. Overall, sororities don't mind giving bids to sophomores, but if they're going to, they're going to give it to a girl deserving of it. There are going to be hundreds of freshman girls coming through for rush who are highly sought after... Say for example, a house is choosing between two girls, you and a freshman and y'all both have the same features... A house will always pick the freshman over a sophomore because they want to have a girl for as long as possible... You need to stand out and show the houses you deserve a bid even though you're a year older.
Recs are always a good thing. You don't need them but they're a good way to get your name out and show the houses that you're serious in rushing.

Rushing as a sophomore is not too bad.
But don't think that because there's an upperclassman quota that you're guaranteed a spot.
You need very good to excellent grades.
Get your recs.
You need some involvement on campus. One or two things is fine.
If you've got a good reputation, keep it. If you've been to campus parties, got wasted, screwed some guys....forget it. They've already put you on the DNP list.
What helps the most is if you have some hometown friends in chapters already. While all the sororities will pledge upperclassmen, they'll only choose a few. It helps a lot when you have friends inside you can keep your name at the top.

How large would you say the sophomore or upperclassmen quota is? I'm sure it's different for each sorority but a general idea would be helpful

It really depends on if you have previously been through recruitment or not. If you have, then it is going to be difficult. A lot of houses have a once cut always cut rule. If you haven't been through recruitment and you have good grades, are cute, classy, dress nicely and don't have a closet of skeletons, then you have a great chance. Get recs for all of the houses, keep an open mind and make friends with girls in lots of chapters. Also, don't tell anyone, not even your best friends, what houses you like before recruitment. This can only hurt you.

I haven't been through recruitment before. A big reason for that was because I'm from the north and greek life is very different there, I didn't realize it was something I would want to be a part of when I got here. I don't really know anyone in sororities other than my roommates, I don't know of any girls from my hometown that even go here. Do they look into classes you took as well as grades? My GPA isn't that great right now (Orgo killed me first semester). Been to a few frat parties but I don't think anyone really knows who I am. For getting involved, I did UADM and some other community service things, and I'm part of another greek organization (not one that affects my eligibility to get into sororities though).