A bottom of the line Nook, Kindle, or other Android tablet (but be careful not just to buy any old brand, and make sure it has Play Store access) will suffice for playing podcasts, and would be far cheaper than an iPod Touch.
There are a good number of apps: BeyondPod, Doggcatcher, Stitcher are probably the most popular. You can subscribe to most podcasts from within the apps and either assign update times, or manually update.