best chances?

Spring is competitive. There are a bunch of girls who feel like they missed out and want to give greek life a shot, but limited spots available. Some houses with openings won't even have open parties, they've probably already planned on bidding friends of other sisters. Right now only 2 houses have scheduled open parties, and they're each taking about a dozen girls. Just go to the parties, be yourself, and decide if you think one would be a good fit. If you don't get a bid (and more girls won't than will), try formal recruitment next year. Then you'll get to see all the houses and find the right sorority for you.

Upperclassmen as in, sophomore or junior? If you're a junior the chances would be slim. Give it a chance but don't get disappointed if you don't get a bid. There is tons of competition.

If you're a sophomore you could probably have a good shot at rushing any one of the sororities, but if you're a junior I'd probably say you should try one of the more accepting chapters, like chi omega or phi sig sig