goal is logistical regression model...where to start

I'm working with weather data using systat software. I have raw values of dependent variable visibility that have been categorized into boolean 1/0 values for whether a range in visibility occurred. The raw values are not normally distributed. I have about 250 possible predictors. I've attached the raw value histogram of the visibility.

My ultimate goal is to use logistical regression to determine an equation that predicts a yes/no answer for the boolean ranges.

I have a couple questions. What's the best initial way to widdle down my predictors to ones that are statistically significant? I thought some correlation analysis may help, but I'm having a tough time determining a good cut-off R value, and the non-normal distribution may be causing problems. I've read pearson correlation should be okay for non-normal distribution. Also should I run correlation analysis on raw visibility values or the boolean values that I actually want to predict in the end?

Next, I've tried running logistical regression in systat, but the output is confusing and documentation not so great. I've attached the output of a logistical regression run.

Thanks so much for any help.