There's some handy ones out there already, namely Geo::Weather and Geo::WeatherNOAA. (I've never used either, so I can't give any reviews).

If you decide to roll your own, yes, LWP would be a natural starting point (use LWP::Simple for ease of implementation, or the main user agent and message modules if you want to learn a bit about sockets, etc).

As for mining the weather report results, a regexp might be the way to go, or you might want to consider using an HTML parser -- this is a judgement call depending on the nature of the page.

The main thing to consider with cron job scheduling is a) automation and b) output. The script must not be awaiting interaction from a user, and results (success or failure) will be appearing in logs or a notification email, so keep the format in mind.

Good luck!
Matt