Just to add to this, I looked up your amp and the spec page says:

"1/4" headphone out/POD 2.0-style direct out for practicing with headphones or direct recording"

This is good. You should be able to plug your amp directly into an interface like Chris and Jeff have mentioned and then plug the interface into your pc. This amp can also handle a mic, this is good as well because whatever goes into the amp (guitar, vocals etc) should go right through into the interface and then into your pc.

In addition, it looks like this amp has varied tones and effects which will help add depth and color.

Audacity is a good choice because of all the DAWs I looked at, it had the best YouTube support.