Bigcozy. . . I've got quite a collection of radios, so pardon my long post. I've found that including SW means you need a larger (though not necessarily huge) radio. I have an older Sony SW-55 that performs superbly. Though this radio is no longer made, it's replacement is the ICF-7600, which has even better performance due to "synchronous detection" circuitry, usually found on more expensive radios. Currently it's selling for about $175 at Amateur Electronic Supply, Ham Radio Outlet, or Grove Enterprises. I've dealt with all 3, they are quite reliable. This radio does NOT have weather band, though!
Careful. . . the radio recommended by Bullzeyebill does not have Shortwave! I've got the older version of it, as well, and the AM/FM/TV/Wx Band reception is quite good. This radio is about the same size as the SW-7600 I mentioned above.
The sony M37 also does not have SW, but again, I own one and I got it primarily for AM reception. It's very good for such a small radio. No speaker is a bummer, but keeps the size small.
Consider the Sangean DT-300VW (available at C. Crane, also a great company to deal with). It's got a speaker, runs for a long time on 2 AAA's, gets AM(really well too!)/FM/TV/WB, but again, no shortwave. Also. . . the headphone jack is a "sub-miniature"(standard in Europe, I think), smaller than a typical Walkman, so you'll either have to use the crappy earbuds that come with it, get an adapter at Radio Shack, or solder your own connector to some cheap headphones. Or, just use the speaker! I really like this radio, it is my travel companion. . . shuts itself off after 90 minutes, so I can fall asleep to Coast to Coast AM!
The only other decent, small radio with SW that I know of is Sony's ICF-SW100. It's about the size of a deck of cards, and though I don't own one, people who do say nice things about it. But. . . no Weather Band!
The Icom R-5 and R-10 are fine radios, but I think you would be disappointed in their Shortwave performance if you really want SW. They do not have Single Side-Band (SSB) detection. This does not affect your listening to foreign broadcast stations, but does not allow you to hear utility or ham radio stations. And I've heard that their general SW performance is not nearly as good as the IC-7600 above.
If you don't know that much about SW, and I've confused you, feel free to PM me, or post. I've been an amateur radio operator for a quarter century now, so sometimes (most times!) I ramble a bit when it comes to cool gadgets like radios.