Ditto on using fraternity over frat. "Frat" is an offensive term to some organizations, so play it safe -- you can't go wrong with "fraternity."
As ChioLu suggested, check with Greek Life as to when you can rush. Some groups at some schools extend bids and pledge year round; others only do so during formal recruitment periods like fall or spring.
As for sophomore standing being an issue, it depends on your campus. My nephew pledged his fraternity as a second semester sophomore before going on to become chapter president as a senior.
I've always heard it's harder to get a bid as a sophomore or higher at the more competitive schools, such as those in the SEC. This is very true for girls going through sorority recruitment (I do a lot of recs for girls attending SEC schools), but I'm not sure if it's as hard for guys. I have two friends whose sons, both out-of-state (OSS) sophomore transfers, pledged fraternities at Auburn this fall, know of a couple of juniors who pledged this year at Tennessee, and have a neighbor whose son -- another OSS sophomore -- pledged a house last year at Ole Miss...so I know it happens at least some of the time even in the competitive SEC! I'm not into tiers, but do know all of those guys pledged strong chapters and large houses as far as numbers go.
Absolutely go through recruitment -- give all the chapters a fair look, meet as many brothers as you can and look for the house that is the best fit for you.