Sasha, I would go for weather channel over short wave, if you have to make a choice...but I would bet all of the radios mentioned here offer both.
Weather channels will give you the up-to-date situation in your area, very important during blizzards, hurricanes or tornados.
With short wave you mostly get Christian radio sermons, national radio broadcasts in English from various foreign countries, or you get a bunch of radio heads talking about their equipment. Interesting, and I'm not knocking any of it, I like to listen to it all sometimes on an old 5-tube Hallicrafters...but not very useful in a survival situation.
My current emergency radio is an old Radio Shack that has AM, FM and WX (weather), takes two D-cell batteries.
I'll say it again, do a little research and find out which local radio stations (usually AM) are going to give you up to the minute news on a local emergency situation. Forget television, they are way too slow getting anything on air and then it's very sketchy and brief.