Most amps will sound quite bad direct to a line in; much of an amp's sound is based on the power section and the speakers.
You could get any of a variety of amp modelers (use the search feature). Or you can get a microphone and preamp. This has a potential for much better sound, but only after you learn to use them, and the sonic properties of your room can be extremely damaging (search for "room treatment).
Either way, you will need some sort of way in to your computer. Your line in will function, but not optimally. You can get a simple interface for less than $50, which will do much better (search "interface").
You can get quite usable recording software for free. Audacity and Kristal come to mind, and I think the original version of Mackie Tracktion is free.