If you're going to buy anything then you should be looking at a DAB+ radio. DAB+ is to digital radio what HD is to a Freeview TV. We've had standard Freeview for a long time, but if you were buying a new TV today then (I hope) you wouldn't dream of considering one that didn't include the extra tuning features to pick up the HD channels as well. Any DAB+ radio includes a DAB tuner too.
Speaking of Freeview, did you know you can pick up a lot of the same stations that are on DAB and DAB+ via your TV? The sound quality is a lot better too, even compared to DAB+. That won't cost you a bean in hardware. It's possible to get these radio stations via satellite and cable too, so if you're a Sky or Virgin customer, or you watch Freesat, then it's worth looking at which radio stations are available that way.
The other really good source for free radio is the internet.
https://internetradiouk.com/ There are radio stations from all over the globe and the sound quality kicks DAB+ into the weeds. It's unlikely that you'll have reception issues either.
Not every DAB/DAB+ station has the licences to broadcast via TV or internet, so there may well be a case for buying a DAB+ radio, but I'd definitely check out whether the stations you want to listen to are available via the other sources because if we stack up by sound quality, DAB+ sits some way below FM radio on all but BBC Radio 3. The less said about standard DAB the better.
If DAB+ is still for you then there are Majority
Little Shelford radios being sold as factory refurbs for £25 on eBay (item no# 363964041188). These have an internal rechargeable battery and include FM tuner and Bluetooth too. That'll come in handy when you have to move away from a power socket to get reception or you have to resort to using your phone's internet connection as a signal source.