Speaking from experience building (not rebuilding) credit, they do look for some history- but it was not very hard for my friend or myself to get the card. I'm not sure of their aversion to baddies, but the 600 cited by the previous poster does sound about right.
However, they will start you at a low limit, because they don't seem to start anyone very high. People usually start at either $300 or $500 from what I've observed. However, they've been pretty good about giving me steady CLIs. I started at $500 in February 2015, got bumped to $700 a few months later, got bumped to $1000 6 months or so after that, and I was just bumped to $1300 about a month ago.
I know that this card does have a bit of a reputation for being a low/no-growth card (and they don't even seem to honor CLI requests), but they seem to be good about giving them out if you actually use the card. I've actually noticed a pattern: I've received a CLI each time I've hit about 15% utilization on that card, and the increases have ranged from 30% to 43% each time. I was actually anticipating my last CLI, because I charged about $180 (18%) to it that month. I don't even use the card very consistently (I use it most months, but sometimes it's just a few dollars), they just seem to care about peaks.
