Voltage source for single transistor audio amplifier

There are a number of things wrong here

1. There are no component designators in the schematic. This makes it hard to talk about, so I'll be more brief than otherwise.

2. You should use junction dots at all points where nets connect. The four lines crossing left of the transistor is ambiguous.

3. A quick calculation of the bias point not taking base current into account results in 1.3 mA thru the transistor, so your claim of 1.26 mA is plausible. However, this should tell you there is no way you're going to get anywhere near 1 W of output power. Even looking at the transistor as a perfect switch, the collector swing will be from 6.6 to 24 volts, for a swing of 17.4 volts. However all this is at a impedance of 8 kΩ. 17.4 Vpp sine wave is 6.15 V RMS. At the best case power transfer, the load is 8 kΩ so the voltage is half that, or 3.1 V RMS into 8 kΩ, which comes out to 1.2 mW. That's less power (although at a different voltaqe) than the MP3 player is likely putting out.

4. The frequency response is a mess. The gain of the amp only 2.7 at low frequencies. This starts going up 3 dB/octave at about 50 Hz, but the high end is unpredictable because it relies on properties of the transistor you don't know. Then the cap in series with the speaker forms another high pass filter, but this also allows the speaker to load the output heavily probably having a reverse effect for part of the range.

5. I can't even begin to guess what the 12 kΩ resistor accross the speaker is supposed to do. It makes no sense whatsoever.

You could successfully build a audio amp from many different types of BJTs. It will be the circuit, not the transistor, that makes the amp work well. I'd pick jellybean parts like the 2N4401 (NPN) and 2N4403 (PNP) and stick with them for everything except for the final power output transistors. Lots of parts could fill that role. If you have your own favorite jellybean small signal transistors, use them if you prefer. The ones I mentioned have reasonable gain and can handle up to 40 V, which should be plenty good enough to allow for a amp to impress your profesor with.

There are lots of possible power transistors to use as the final output. If you are aiming for a few Watts, I'd probably go with basic parts like the TIP41 (NPN) and TIP42 (PNP).

Again though, it's not the choice of transistor that will make or break this project. You can certainly create a impressive audio amp with the transistors I mention, but you can also make a mess. It's really up to the design. In audio, overall noise and harmonic distortion are high priorities. Those come from careful circuit design and attention to these parameters at every step along the way.

You can also use other types of transistors, like JFETs or MOSFETs. Those would require a different circuit topology to utilize properly, but can be used to make a good amp too. Since you will be going over BJT details more thoroughly, I'd stick to them for now. This will be a great learning exercise. Designing a amp with very low noise and very low distortion is not trivial.