You can personalise the radio stations you see in BBC iPlayer Radio by visiting the Edit Stations page and selecting the stations you want to see. You can add any National station (such as BBC Radio 4), Nations stations (e.g. BBC Radio Scotland) and any Local Radio station (e.g. BBC Radio Leeds).
You need to be signed in to BBC iD in order to do this, but once you have done that you can access your personalised list of stations from all your computers in different locations.