I would like to listen to pod casts in my potting shed

HP_Source

I'm sure that's the right approach, Alicef. As you've probably gathered from the differing answers there's no one solution - it's a matter of finding what works best for you.

I had the same dilemma when I wanted to listen to music while working in my shed but there was one added complication. I wear hearing aids! I've ended up with a wireless access point on one outside wall of the house, and old mobile phone in my pocket and a pair of over the ear noise cancelling bluetooth headphones.

twopenny

I've got an old kindle for £25 to listen in my multi purpose garage.
It's small and light. Would fit into a work belt or carpenters apron pocket for use with headphones but the speaker is nice and clear.
I didn't sign in to Amazon when prompted and it works well for running podcasts..
It seems to pick up my basic old wifi but I can also download in the house to listen elsewhere.

I also bought a second-hand old phone for the same purpose. No sim but just use wifi.

If you want something small with sharp sound I have an mp3 player but have to download to computer and transfer. Tiny, very clear both blue tooth or headphones and the battery life is double a phone or tablet.

alicef

Thank you to everyone who made great suggestions. 

Using my tablet plugged into power in potting shed, with downloaded podcast and my existing bluetooth ear buds, I managed about 25m distance from tablet before sound broke up, so that is pretty good to be going on with.