You want producers or agents to be on the jury, or you want to know that the winners will be somehow publicized in Hollywood - probably an announcement in the trade papers Variety or the Hollywood Reporter. I know one writer in Los Angeles who, frustrated with trying to get her script read, rewrote it as a play, found a theatre to produce it, and invited every agent and studio executive she could think of to opening night. She eventually optioned one of her scripts. Finally, yes, people like myself can act as a conduit between writers and producers or agents, but there's no established route here. It would mainly be a situation where I might happen to personally like a script well enough to want to get behind it and pass it along to an agent or producer in Los Angeles.
Readers absolutely have an influence on which films get produced.
I look for a story that makes me forget that I'm reading a screenplay. The thing that most determines whether I recommend it or not is the personality of the script. Even if the story-line is not earthshakingly original, if the characters have depth and believability, if the overall feel of the story has resonance, then I would certainly recommend it. But it is very nice to read a script that keeps you guessing. Every project is different, but in general, the work of a development executive begins with writing story notes on the screenplay.