easiest way is to get an ipod shuffle - £30 odd pounds and dowload itunes to your computer then put your cd's there and buy itunes.
If it is just podcasts from t'internet you want then any ole mp3 player £10+ will do the job. It's a bit funny with downloading any itunes that you have bought. but if you dowloaded your own music onto itunes then it would let you put it on there
Any MP3 player will be sufficient for your needs, if you are not going to be visiting the online stores to download music (some seem to work only with iPod - though many tracks work with any player).
Given the low cost of an MP3 player, I would suggest getting one of those initially and seeing how you get on. Reddmango 1GB MP3 Player is £10 at Argos. If you find that the music you want to download insists on having an iPod, then you will need to consider getting one of those (could be got for you as a Christmas / Birthday present - iPod Nano for example.).
Audio from the BBC website is often available in MP3 format. You save that file to your computer then copy it to your MP3 player.
To import any music already on the computer use import folder under the file tab in itunes. To import any other music, put a cd in the drawer and it should ask you what to do with the disc. There should be an option to import it using itunes. When the music is in itunes, you connect your ipod, click on tracks you want and drag them to the ipod icon.
iTunes is an application you can download. It will run on your computer without an iPod. It will convert CD Audio to MP3 files. You can then locate the MP3 files on your computer and copy them to your MP3 player. If you have an iPod then copying files to it I believe is a lot easier.
If you are not on a tight budget, go for the Apple iPod Shuffle to start with. It is more expensive than a basic MP3 player, but it will make life easier if using iTunes.