First of all, I am an absolute beginner. I'm going to be developing a game for a Nintendo console completely by myself and I don't know where to start with sound design. What software should I use when I'm just starting out and should I eventually upgrade to something more complex when I get better? Then I'm looking for tips about that software and sound design in general. I'm looking to create music and sound effects so I need some advice on both. Any advice about how to start writing a song? This to be cautious of? Things to avoid completely? My favorite composer is Koji Kondo so I'm looking to create music like his if that helps.
Your questions couldn't get much broader, especially as the reader isn't aware of what precisely you are a 'beginner' at... There is so much to cover.
You haven't stated whether you already compose anything. Without knowing this, it's difficult to know where to start, on the music side of things.
Do you wish to emulate the 8-bit sounds of a NES? I'll assume so, for my entire answer... In which case, you should utilise square waves, 12.5% pulse, 25% pulse, triangle waves and 8-bit noise. You will be able to find plugins designed specifically for this task (Google is your friend). The use of arpeggiated chords/runs, unison and vibrato will emulate typical early video game music (though Koji didn't use fast arpeggios all that much).
If you wish to emulate Koji's early writing style: He predominantly wrote in a major scale. However, he has some jazz leanings. He often changes between major and minor in the same riff, and will introduce a minor sixth whilst otherwise staying in the major scale. He tends to focus on expressive, memorable lead lines... and the accompaniment is often a counterpoint, or plodding bass line. He is fond of descending chord structures, that switch scales for an uplifting, or melancholic emotional effect. He often manages to create this melancholy feeling from his brief deviations from the major scale. He takes some cues from classical music (counterpoint arrangements) some from jazz (scale/key changes, atonal parts, odd time signatures).
If you have never composed before, you would likely be able to make something simplistic, but it will possibly fall short of the rest of your endeavour. If it is a professional/paid project, I'd consider employing someone, if you're new to composing.
Sound design in 8-bit is very limited, which stands in your favour. The use of noise provides all transients (other than pitch sweeps) and explosions etc (with a low triangle etc beneath). I could write more on this but I feel you can easily figure out how each sound is made that you hear in original NES games. If you struggle, take a look at the waveforms themselves, after importing them into your DAW.
I hope I've started to answer your questions. Good luck.