I got a jack-to-USB cable from my mother, as a present.

I've already tried to record some things, but I've noticed that the sound very easily clips, I need to keep my guitar volume knob at less than 6-8 depending on the amp model I use (Amplitube, Reaper, anything).

When I googled a bit, I read that the connection between the guitar and the computer via the USB port skips the sound processor, but I have my doubts.

Should I buy a sound card/interface, or is it something else ?
I hook my rig directly to a small mixing board and output the mixing board directly into my sound card and use adobe audition 3, you could easily get by using a freeware such as Audacity, but I noticed a huge difference from a board rather than a pedal to a usb, it's just easier to control. Mixers now a days also have a usb connection also. To me it's just easier to control off the board than tweaking the interface to your liking.
you should use an interface that has a gain knob, so you can control the clipping. Also, when you use your computer's stock sound card, you get very high latency (you can't play and listen to the computer at the same time, because there's a delay). I recommend getting the Steinberg CI2. It has two inputs (2x Mono, or 1x Stereo, both are XLR and 1/4" compatible), and best of all, it has its own sound card with almost zero latency.
If you have any specific questions, you can PM me.
Yeah an interface is the way to go. There are cheaper ones (sub $100) that are for only electric guitars, but if you think you'll ever want to record any other instruments/vocals sometime in the future, invest a little more in something like a Fast Track MKII.
All right then, interface it is. I have to wait till September until I can buy one, but I think I will go for the one you suggested Eatfresh. It works with more than just Cubase, right ?