Older iPod Touch

I am not very familiar with the iPod Touch's generational bumps over the years, but am looking for something to serve as a music player, almost exclusively on Rhapsody (or another cross-platform service if I ever change), largely playing music out of local storage. It needs to be under $100, which seems to mean 3rd-gen. The device looks great for my needs, but I don't know if there would be any problems, including with the OS or running the limited software I'll be using. Also not sure if typical battery age would suggest limited life.

This is a very discretionary purchase since I already have a smartphone (GS4), but a separate, smaller PMP would be great for the gym and in the car, and for sharing between family members on different occasions. It's limited use, so I'm not planning to spend a lot. I could probably find a decent 3rd-gen for $80/90 shipped and a 4th gen would be about $120 shipped, does that sound right?

Thanks for any advice!