Plugging something into the headphones jack on a guitar amp usually kills the speaker, but not always. I actually have an old Marshall combo that has a headphones/line out jack. Plugging something into it does not effect the speaker. Some amps have an actual line out, and not a headphones out, so that would be preferred. But if you're using the headphones as a line out, you'd be able to listen to your guitar through your PC speakers as you're recording.
USB interfaces are great. I have this one:
http://tascam.com/product/us-200/overview/
Comes with Cubase LE for free. Most USB devices like that will come with some free software to use. Cubase is alright, but I'm still using Audition. Here's something I did with that Tascam and Audition for example:
A USB interface will yield better results, and allow you to do more. The above recording, the guitars and bass were recording direct into the Tascam (no mics). Also, it gives you the ability to use an XLR input which PC sounds card obviously don't have.
But using the line in or mic in on a PC's sound card is perfectly fine for quick recordings. If the line in isn't working out for ya for whatever reason, you can just use a cheap PC mic. They don't all suck as bad as you would think. There's this one that use to come with Dell PCs...
http://www.ebay.com/itm/Dell-Black-Plug ... 484f8b87db
They're actually REALLY good for what they are. They sound very decent. If you're not looking to spend any money, that's what I would do. Otherwise, the USB interfaces are awesome, and an SM57 is about $90 (or less if you buy one used).