Well I spent some time getting it all together and lo and behold, it works! I'm not sure how well it works, but it does get fairly loud. Almost as loud as my cell phone at max volume but it sounds a lot better. My cell is kind of tinny sounding, but the amp I built has a bit more "depth" to it, I guess... lol.
As for the gain, yeah, I only need a voltage gain of a little over 4 in order to drive the speaker at 1W. So I'm not too worried about distortion being an issue, really. I just figured if I could do something to help a little bit, I'd go for it.
Alright, so, I just want to say thanks for you all your help! People like you are what make this community great! I'm really glad you took the time to help me :)
As a last question, are there any books or learning materials you would recommend specifically for transistor amplifiers? I'm interested in Class A, AB, etc... not so much class D or anything like that. I saw this book on Amazon and thought about getting it. I'm not well versed in mathematics, but am slowly learning. I have studied linear algebra and a little bit of trig, though. But calculus is still a ways off. And I've been told it's not that necessary anyway. Linear algebra can get you pretty darn far.
I've attached a picture of the amp on my breadboard. Check it out!
It would be possible, yes.
It would also be difficult and complicated, and the resulting audio amplifier would not be "Blameless" to use the category name from Douglas Self's amp design handbook
You would have a far FAR easier time designing an audio power amplifier using the most modern, rugged, high gain, LINEAR, matched complementary bipolar transistors available: the MJL3281(NPN) and MJL1302(PNP)
They cost four dollars (link) and you need four of them for the left channel, plus four more for the right channel. This will give you 100 watts RMS continuous power per channel if you competently execute the design. Perhaps by following Self's Blameless procedure.