Any of the technologies you mentioned could get the job done with varying degrees of work and performance.
I personally find myself following a different route based on pieces I have built. First you must know that I wrote Bitlash, an interpreter for Arduino, and so I think in terms of sending Bitlash commands from the PC to control things on the Arduino side. The idea is similar to what TanHadron suggests. So I usually start with Bitlash on the Arduino side, at least for prototyping. (More at http://bitlash.net
Then I wrote an app called Bitlash Commander to control the Arduino from the PC by sending commands from a web browser. This is kind of like the program you will need, to fetch weather data and send it over the serial link. (More at https://github.com/billroy/bitlash-commander
If I had to start on your problem today I'd probably work up a little node.js script similar to Commander to do the weather API fetching, parsing, and serial transmission. Plus a web control panel for the display...
Whatever you're comfortable with, right?