Will you have accommodation fixed up when you arrive, or will you be in a hotel for the first few weeks?
If the answer is hotel, then you probably won't have the internet option, at least at an affordable price. Even if moving straight into an apartment, it can take time to get your internet sorted. Due to the hilly nature of this land, radio reception can be pretty dire if you are in the lee of a hill - I can only get one station with satisfactory reception over the airwaves at home, and it's a station I detest.
Now the good news

Most properties here have cable TV and radio plumbed in, and I would expect that any decent hotel will have that. Budget hotels might not, so beware, and when searching for an apartment a key question to ask is whether a place is connected to the cable network.
Now even better news. I've just looked up the analogue cable radio stations provided by Cablecom in central Basel (post code 4000), and I see they do
BBC Radio 4 (scroll down to see it).
My advice would be to not rely on your DAB radio and get an ordinary FM one with a cable socket. The January sales are a good time to shop for electrical goods here in Switzerland, and remember that VAT is only 7.6% (if I were in your shoes, I'd sell my DAB radio in the UK and buy new or even second hand over here until you get settled in).