t-p,
The first symphony, written while he was still a student, already has an unmistakeable Shostakovich sound; the next two, which are perhaps symphonies only in name, are rather wild experimental works written for specific state occasions, breakneck collages of all sorts of ideas apparently thrown together rather like a choppily edited film, perhaps not inappropriately for a young man who'd spent his teenage years playing for the silent cinema (although the more detailed work I'm doing on the second is starting to reveal more of a structure than I'd first identified). I've already suggested that the choral finale to the second has Mahlerian scale and progressions, whereas in the third it's not so much the choral finale (which always strikes me rather more as Beethoven 9 meets the Red Army Ensemble) as a tiny but very Mahlerian adagio passage which is fragmented and interrupted rather than allowed to develop - not that anything in either of the two is really allowed to develop.
As others on this thread have pointed out, the fourth symphony is probably the most Mahlerian of the whole sequence, with echoes of the birdsong, of the Viennese Ländler, and the depth and range of his symphonies. Not a slavish copy in any way, but there's an unmistakeable flavour of Mahler at times. As must also be very evident, I have become particularly captivated with this work, which seems to me a masterpiece of the highest order, capable of being listened to and studied day after day.
Since there was an entire cycle of the symphonies on R3 last year, it's rather unlikely that you'll be able to hear them all on the radio again soon. The rarer ones really don't turn up all that often, though the middle group from (5 to 11) are broadcast rather more frequently. CDs on the other hand, could be an easy answer. Several complete sets of the symphonies are readily available, some very cheaply. By and large most of the regulars here would recommend a Kondrashin cycle as first choice, until recently not easy to come by in an edition from Korea, but very recently much easier to source in a new reissue. If you don't have much spare cash, then the Barshai cycle, though far from perfect, is rarely less than acceptable, and often available at rock-bottom prices, as here;
http://www.amazon.co.uk/gp/offer-listing/B00005UW2B/ref=pd_bbs_sr_olp_1/202-4411543-5828653?ie=UTF8&s=gateway&qid=1176759825&sr=8-1the set doesn't give you absolutely everything that the symphonies hold, but it's not a bad introduction at all.
There are also sets by Rostropovich (haven't heard all of them yet, but like what I have heard) and Jansons (sorry, doesn't work for me at all, though I seem to be in the minority) available at a good price: though whatever you buy, if you take to the symphonies then eventually Kondrashin will prove a must. When we get down to individual symphonies the choice widens, but the one name to look out for is Mravinsky, who was the other great champion of Shostakovich's music, though he only ever performed the works which weren't considered controversial because his wife was an important party member and there could be no upsetting of the apple cart. So there was never a Mravinsky performance, let alone recording of the fourth (even after its première a radio broadcast was forbidden by the party because it was still felt that the piece was too dangerous for mass consumption) nor the thirteenth, for example....