It's hard to get into the details of particular sounds, but I'll touch the basics here.
First off, keep in mind that there were several chips in the good old 80s. While POKEY was used in several home computers and a few arcade hall machines, it doesn't mean you will be able to emulate all the sounds you remember from that era. For example, this chip has square waves by default, but not sawtooth or sine waves. Of course you can't ever expect it to emulate realistic sound effects.
What all those 8-bit machines had in common is that sound effects were created by updating any of the sound registers during the screen's vertical blank (usually at 50 or 60 Hz). So you have decent flexibility to start with at a room speed of about 60, changing the sound registers at every step. There is no point anyway to make more calls to gmpokey_sound()
than once per step, per channel. GM's timing is though less than dead accurate, you have to make sure that the frame rate is constant.
Sound effects were a matter of creating frequency and volume envelopes, and concatenating sounds with different distortions. To speed up the process those envelopes values were sometimes stored in arrays. For many sound effects more than one channel was used, although the 'real' art was in making sounds as complex as possible using a single channel, saving other channels. For example, arpeggio was used to create a chord sound of 3 notes on a single channel, by alternating those notes with pauses of about 2 frames between them and repeating that sequence (so you hear a very quick succesion of those 3 notes).
Most of the popular sound effects usually apply a combination of square wave (distortion level 10, good for jump, fall, die, and other beeps) and noise (distortion level 8, good for shots, explosions, hits). Machine-like sounds can be found in distortion levels 6 and 12. There is no rule of thumb to the sound effects though - except that for good sound effects, you will always apply at least some frequency, volume, or even distortion envelope. An unchanged single sound will never do.
It helps to listen to real sounds to make a kind of chip counterpart. Does the frequency go up or down, where does it start, how fast does it go? Is it noisy, clear, a combination of both? Does the volume fade, increase? How loud does it start or end? Et cetera...
Of course, the sound you produce is only a suggestion... The game player only associates it with what happens on the screen, and the imagination does the rest.