If 48 dB is what the teacher wants, then give the teacher 48 dB...get the grade first, then modify the circuit later.
NFB is common shorthand for Negative FeedBack--saves having to write it all out.
Output networks are just there to stop oscillations. If, by some miracle, you've got a circuit that's stable without one, then by all means don't go mucking up the sound with a bunch of extraneous nonsense at the rump end of things. Basically the intent is to short high frequencies to ground with a cap and/or stop them from going out to the speaker with an inductor.
Input coupling caps are to be avoided, if possible. The best cap is no cap, and all that. The concept is that you want to block possible incoming DC that might either change the operating point of your front end or show up at the output of the amp as a really huge DC offset that will turn your woofer's coil former into something resembling popcorn. The decision is yours to make--sound quality vs. safety. Me, I regard all components as guilty until proven innocent. I've heard far too many things chipping away at my signal quality that "shouldn't" be doing so. Good quality caps aren't nearly as bad as some other nasties, but I still prefer to avoid them whenever possible. Besides, they're bulky and expensive. On the other hand, I lost a subwoofer driver once upon a time when the rail in a crossover got loose and went through the amp. You pays your money and you makes your choice.
Regarding bandwidth vs. gain, I assume you're referring to a Bode plot. Yeah, all things being equal, lower gain means wider bandwidth. But...things ain't always equal. The "Specifications Are Everything" crowd run the gain up to where you can look someone on Mt. Everest eyeball-to-eyeball, then knock it back down to something reasonable by using lots of feedback. They feel that NFB does no harm to a signal. I've got a different view, in that I've played with circuits and listened to the subtle things that NFB can do to a signal. Most solid state amps get rather spastic if you try to run them open loop. Tube amps are much more polite beasts and are quite happy to run with no feedback whatsoever. All you do at that point is add a pot in place of a fixed resistor and play to your heart's content (being sure to readjust the volume, as adjusting the NFB, by definition, will change the gain of the circuit). My advice is this:
--What kind of music do you listen to? Rock/pop/rap, and the like? Most (there are a few exceptions, but not many) recordings of that type lack the kind of detail that NFB destroys. Go ahead and use all the NFB you want. Bluegrass, classical, jazz? Use only enough feedback to get the job done.
--How's the rest of your system? Party machine? Mid-fi? High-end? Choose lots of feedback for party machines as the damping will increase. If you have now, or intend to have in the future, a high-end system, consider going lightly on the NFB.
Beware--if you shoot for mid-20's dB gain, and intend to get there from where you are now using feedback only, you're building an oscillator, not an amp. It'd be really easy to tune the gain in at, say, 26 dB by adding 22 dB feedback on top of what you've already got. Your bandwidth will go from DC to light. Somewhere around 50-200kHz you'll pick up a nasty oscillation that will make short work of your tweeters. There are various ways to approach this, but a good place to start is to build in a rolloff at 100-150kHz, then add a network at the output.
The more elegant solution is to design less gain in from the git-go (thus hitting lower on the Bode than you would otherwise), then use NFB sparingly to fine tune the circuit, rather than as a hammer to bludgeon the poor thing into submission.
But the more immediate goal is to get the grade. Turn in a circuit that makes your teacher happy.
Grey