You could really do all this with a USB sound card. There's software that will let you use one as an oscilloscope. There's also software to turn one into a distortion analyzer, plus a signal generator!
You'll need to create some attenuators to bring the voltage from the speaker outputs on your amp to a level safe for the USB sound card, but that's not hard and can be done with nothing more than a few resistors.
I'm with Tim regarding using your computer's audio output for your signal generator. There's a variety of programs available for generating tones. Alternatively, you can use an old MP3 player, outdated smartphone, etc. to play audio tones that you create on your PC.
I'd be a little more wary about using the computer's audio input as an oscilloscope right now, since you're new to scopes, unless you're using it with a very inexpensive computer that is OK to fry (only accidentally, of course).
In my original post I recommended a USB isolator to protect the computer. They're fairly inexpensive and will galvanicly (or capacitivly) isolate the computer from the sound card.
Most of the inexpensive ones use an ADI chip that's good to at least 1kV; the more expensive ones use an LT chip which isolates to a higher voltage, but that would be overkill in this case. (The LT chips are pretty awesome though; they actually etch the isolation transformers into the substrate of the chip!)
The other approach would be to hook the sound card to a Raspberry Pi and use some remote USB port software. Basically you install the driver on the Pi and then on your Windows/OS X box; it actually adds a "Virtual" USB root interface. Then, when you plug a USB device into the Pi, all the data is transferred over Ethernet to your PC and enumeration happens there.
It's pretty slick and actually works fairly well. I'm not sure how well it would work for a device sensitive to latency like a sound card... But on the other hand I've seen it work with webcams, so maybe it would be OK? I might give it a try this evening, just to see... (I actually ran all my USB test equipment this way; that is I plug them into my Pi and can access them from any PC/Mac on my LAN.)
As to the OP and an analog scope, I'm not sure how much that will help him... Sure, he can see clipping, but he can't really do distortion measurements (at least in any meaningful way). Plus there's no FFT...
For the $50 + shipping price of an analog scope, he could buy a USB sound device, isolator *and* a multimeter!
That would serve him well enough to learn with, while he saves up for a digital scope.
I'm not doing anything with my computer it's only a year old and not going to use it for something with this audio stuff not trying to be mean or anything just I don't want to use my computer for any of this stuff.
That's not a realistic option, sorry.
Keep in mind that professionals who design and repair audio gear almost always use a PC with some sort of external interface (be it an Audio Precision System One, or even a $70 Behringer UM2 USB Audio Interface+TrueRTA software).
In the end, to really do what you want, you're going to need to use your PC. You'll obviously need a scope as well, and I didn't mean to imply you didn't.
That's why I recommended starting out with just the PC, as you can get some software to turn the USB audio interface into a scope as well. However, if you're not comfortable with the idea of making your own attenuators and such, then by all means just get a cheap analog scope! Like someone else said, having a real scope can open up doors to other areas of electronics.
The analog scope will show you clipping in various parts of your amps, and you can use it to get a rough idea of the noise floor, but you won't get any sort of precise numbers out of it.
If you want to actually see your THD or THD+N %, or measure actual frequency response, you basically have two options:
1) Buy thousands of dollars worth of vintage test gear (spectrum analyzers, distortion analyzers, etc.)
Or
2) Use your PC and a 24/192 USB Sound Card, plus an analog or digital oscilloscope.