Electric guitar recording-directly to computer or through amp

I just got a new-to-me PowerMac G5 that has Garageband and wanted to figure a few things out before I started buying stuff that I don't need.

I would like to record music to Garageband and play around with the software and hopefully create my own music. I am not a good musician so this doesn't need to be a professional setup, it is more of a hobby but i also don't want to put in a bunch of time into something that is always going to sound low quality because of how i am recording the music.

I have an electric guitar and a small fender amp, and maybe someday will move on to recording vocals. As far as the guitar goes, it seems that I can either plug it directly into my computer, or run the guitar through my amp and then into the computer. What are the advantages and disadvantages of each method? Like I said, I'm not going to be trying to get signed to a record label or anything, but I am willing to spend a little money if i need to so that the quality is good.

I just want to start out the right way so I don't spend money on things it turns out I don't need. Just basically looking for a startup guide to recording my own music through Garageband, but everything seems to be about software, I am more concerned with questions about the instruments and hardware.

Thanks for the help