How many minor characters/side characters (whatever you call them) is it a good idea to have?

As many as are needed. The trick is to avoid duplicating roles within your story. So, for example, in my novel, I had the MC's best friend, her over-protective friend that drove her to a certain location and the gossipy friend who gives background information. It turned out that I didn't need all of these. I could just combine them into one character, so I did. Each character should have a distinct role. If you can combine characters together, then do so. Characters should be able to multitask within reason. (eg: You can't have the gossipy, shallow friend also be the character who is being gossiped about by herself.) The fewer the characters, the more likely your reader is to remember who is who, and remember the details of their lives.

As long as each character has a role and it's clear cut and well-defined, you can have 20 side characters. Or 200. Figure out what your characters need to do, and figure out if you can combine any together to keep it simple.

Good luck!

Your cast of characters should only consist of people who do things that move the story along. If a character doesn't have an important (not necessarily large) role to play, they can be dropped without harming your story. If a bully doesn't really matter to the plot, ax him.

One caution though: beware of straw men. This means you have created a character who has only one function. You are not interested, as a writer, in fleshing out this guy, you just need him to yell "FIRE!" or whatever at a critical point in the plot. If you can, assign jobs to characters who are otherwise important to the plot. Straw men don't add anything.

It greatly depends on the story. Some stories require more while other's don't need very many.

If you can handle all six individuals with different personalities, and make them all relevant to the plot, I don't think that is in any way too many.