This will affect your judgement of what copyrighted material you will use. The level of risk (whether it is high or low) may inform what you do with copyrighted material, i.e. what and how much of it you use; but you should always consider whether your usage is fair to the copyright owner (see the Fair Dealing part of this guide).
Use copyright free sources, which are available in different styles; sources include:
With resources like these:
If using as background music, don't choose music with a no-derivatives licence (ND), which doesn't allow changes; using music as an accompaniment to video material is considered to be a change to the music.
Acknowledge the recording as instructed on the source website.
Use as little as possible, and no more than necessary. Make sure that you haven't affected the market for the original. This means that you've effectively made it unnecessary for anyone to purchase the music by reproducing part of it; this could for example be because the extract is quite long.
Ensure that the purpose of reproducing it is absolutely clear, and it is relevant to the topic
Don't use as background music
Cite the piece of music and the recording (see Cite them right below).
Parody/caricature/pastiche: using and transforming part of a work for humorous purposes is allowable, but make sure that the purpose is justified (i.e. directly relevant to your work). For an academic assignment it is likely to be, as you will be guided by the requirements of the assignment. For podcasts to be made openly available, you will have to consider this more carefully. More information on Parody and Pastiche is found on the copyrightuser.org website.
Although podcasts are most commonly perceived to be audio, video podcasts are becoming commoner.