Others might have more expansive insight or technique to add, but so far in my journey, here's how I avoid or minimise squeal.

For any particular setup, do use string lube, have clean hands, use no more fretting pressure than necessary & relax pressure as you move (requires conscious awareness at first becomes instinctive with practise & experience over time), use less gain on cleaner settings. Squeal is contingent to all the above. Most evident on cleaner settings. Distortion will hide it.

Amp buzzing (vs string buzzing) is largely excessive gain, which is exacerbated by cheapie electronics, e.g. output jack, switches, pots, including poorly shielded constructed instrument leads. If you are referring to string buzzing caused by fret interference, it could be as simple as your action or a string being too low, through frets which aren't level due a number of potential causes.

Have your guitar's action set up so it is not excessively high is important (fretting compression distance and pressure), and check frets for level. String gauge (tension) is relevant as well (squeal).