So this is probably a dumb question, but could I record my guitar that way:
-Plug the guitar into an amp
-Plug a mixer to the line out of the amp
-Then plug a guitar interface to the line out of the mixer, then the interface to PC
Would that work/sound good or is it better to just mic a cab?
It would most likely sound terrible if you do it that way because IIRC the line out is simply your preamp sound. Your tone isn't getting colored by the power amp or the speakers so you'll have to do extra tweeks to get it sounding usable (IE Impulses, EQing etc...) Either mic up a cab or plug into your interface and use VSTs.

Is it doable? Sure but I personally wouldn't do it that way.
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Word. If you're new to micing up speakers look up mic placement articles and stuff and experiment to get the sound you're looking for. No question is dumb if you're looking for real information, man. Best of luck.

EDIT: This is a good place to start.