Best transistor to use for audio amplifier

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.

You will probably make a more effective power output stage using BJTs for the same number of components compared to MOSFETs. I use the word effective to mean that your output voltage will swing higher/bigger for the same power supply with BJTs used in a simple push-pull circuit. This is because, to turn-on a BJT, you only need about 0.6 to 0.7V whereas to get a MOSFET supplying several hundred milliamps you might need to drive its gate with 3 or 4 volts.

Again, this will be a simple emitter-follower push-pull class AB output stage. You can only drive the output transistors with a signal that is restricted to the power rails and if this is (say) 24V dc - you should be able to drive a signal that is 22Vp-p to the power transistors. Given that each BJT would "lose" 0.7 volts (because of the base emitter junction), the maximum output voltage will be about 20.6 volts peak to peak. If you were using mosfets, it would be more like 14 volts peak to peak into a decent load.

There is a bit of hand-waving in my answer so far but, just do your homework on mosfets connected as a source follower and pick one with the smalled Vgs(threshold) and examine the data sheet to see how much gate drive voltage is needed to get a few hundred milliamps flowing through it.

There are more complex designs that are quite difficult to get working where the output transistors are collector-connected or drain-connected but, for a beginner I'd stay away from these because they will be unstable if not carefully designed and, require more silicon to get working effectively.

So, given that you haven't specified power output, speaker load or voltage rails I'd say a BJT power output stage is probably the best choice. As for the other transistors I'd stick with BJTs - they've been used in tens of thousands of good commercial designs. You could of course consider a class A output stage using an output transformer - this is probably worth considering but the down-side is the loss in efficiency due to the final transistor biasing.

I've just had a look around for a fairly simple output stage that shows the biasing arrangement you'll likely need for a decent amplifier and came across this one: -

It came from this site. I'm recommending it because it seems to have a decent spec and the site also recommends a cut-down version without the diodes/biasing. I personally think it would be a good start for a beginner. The site discusses several things about what is needed to make a good output stage.

You can take the basic design and add gain to it and swap the op-amp out for individual transistors if you do a bit more research.