Hi Genevieve! The way I understand your query is that you are going for a really simple, yet durable player. I'm not sure if you have a preferred budget range.
Anyway, I would highly recommend the Sony NWD-B103 player which was recommended by alphaben earlier. It is light and durable because it's made by a trusted brand. I know it has a radio feature but you can always not use it.
Cheers!