Here are my two cents on what to look for (I don't know the answers)
* Who are the partners behind the fund, what have they done in the past (pre-investor) and what is their core skill (tech, product, marketing, sales, operations)
* Who have you previously invested in, and where are they now?
* Who are the limited partners of the fund - did any VCs/rockstars/partners invest?
* Why are you superior to Y Combinator? Startup accelerators are very popular now. They generally have the same mentors, the same deal terms, the same investors come demo day, the same "industry connections", whats your USP? (some good answers here might be specific domain knowledge of partners, a strong alumni, and so on)
I am always bullish when sites list such an array of mentors because being a mentor is generally high upside (fame/feel good/networking/karma) and very little downside - no skin in the game, as it were.
A buddy of mine once told me that equity was "quick to give away, impossible to reclaim" - you're giving these guys a significant % of your company, be sure they're good - and there is nothing wrong in applying for dumb money. Just don't tell them that.