What would be a good, but inexpensive microphone to use for recording mandolin songs?

Shure SM-57. It's the industry standard mic for instruments of all types.

USB mics are ok, great for podcasting in fact, but all have one limiting factor: your computer's internal sound chip which is what they will use to process the sound. And on most laptops, that little chip isn't going to yield professional results. So the Samson you're looking at is good but will give you demo quality recordings but not professional sounding recordings.

I know you're budget conscious, but the best way to record on a laptop is through an audio interface. They use their own built-in AD/DA processors and mic preamps. This will give you both a better recording and the benefit of a wider selection of microphones.

A good budget Audio Interface is the Yamaha AudioGram 3. It comes bundled with Cubase AI, a good digital audio workstation (DAW.)

A good budget mic for recording acoustic instruments is the AKG Perception 120.

The AudioGram 3 is $99 and the AKG Perception 120 is $63, plus you'll need a mic stand and an XLR cable which brings the total to a little over $200. Still, this set up will yield professional results and give you tools on your computer to add multiple parts and keep them all in sync.

If you own no other recording equipment, get a basic USB condenser mic - USB mics connect directly to your computer with no other equipment needed:

http://www.amazon.com/Samson-Track-Microphone-Audi...