A great way to obtain an excellent MP3 player is to re-purpose an old smart phone. I bought an LG 800 (new in box) off eBay for $10 with free shipping.
Just don’t activate it (unless you need a phone, that is). It will come with a micro USB charging cable. Charge it up, slip in a micro-SD card, put it in airplane mode (longer battery life), and presto you have an excellent Mp3 player. I have used one for over a year now and love it.
I suggest adding a grippy style cover so you can hang onto it. The protective cover will just cost a couple of bucks and you can even install a lanyard to keep the small phone around your neck while working out.
The LG 800 has a full size (3.5 mm) stereo audio jack, so no adapter is needed. Just plug in your favorite set of ear buds or headphones. The music player works great and has a slider, so you can easily jump to different parts of a podcast/audio book. I have had purpose-built MP3 players before that made this nearly impossible; you would have to sit there holding the fast forward button for 5 minutes or so.
After a few seconds, the screen will go blank while playing audio files (to save battery life), and so that you don’t accidentally turn it off or skip forward or back. Just push the center button and another onscreen button to access the music player app. An attractive “now playing” screen shows the cover art with a slider and rewind/FF buttons. Volume adjustment is done with a toggle button on the side of the phone.
Besides being able to play podcasts and songs, you also get a built-in camera, calendar, to do list, memo pad, alarm clock, and many other functions. It does not have wi-fi, but if you want your re-purposed smart phone/MP3 player to be able to be used as a small tablet, just skip the LG 800 and go with an older Android smart phone that you can buy for $30 or so on eBay. But the LG has inherent advantages — better battery life (about 10 hours of continuous listening) and it is small.
To get content onto it, simply connect it to your computer and allow it to go into connect mode — at which time you can drag and drop Mp3 files into it. This will keep an older device out of a landfill and will serve you well as a modern “Walkman.”
[Some cheap phones on eBay have "bad ESN" (electronic serial number) in the description. It is a hassle to activate a bad ESN phone with a mobile carrier, but you can still use it as an MP3 player. -- Mark]