First a bit of food history. I love this stuff. Minestrone comes from the same root as does ministry, i.e. to serve. The minestras were the serving people in Ancient Rome, and what they got to eat was any leftovers from preparing meals, or food returned to the kitchen unfinished. They survived on this and so can you.
So minestrone is a "throw it all in" soup, which means there is no recipe for it. What? But I can find hundreds of recipes for minestrone online! Sure you can, and they're all different. You'll find a favourite sooner or later, but you'll also discover you can make this out of leftovers/what's on sale/what's in the garden in a glut/what needs using up in the fridge, etc.
So a question arises, when is a soup NOT a minestrone? Well, that's an argument you can have all day, but in my opinion the guideline is as follows:
Minestrone is a hearty soup, with a lot of different vegetables, possibly meat (but not essential), and definitely including beans, but also possibly pasta or rice. It usually includes tomato but that's not essential. Served with bread, it's substantial enough for a main course meal. It is also my considered opinion that as this dish originates from Italy, then flavourings should be those typically found in Italian cusine, in other words, if you used Indian or Mexican spices, it ceases to be Minestrone (but it would still be most excellent).
Because it can be varied so much, it's possible to slip this into the dinner menu weekly, or even more often, without the family crying "Oh no, not again".
Here is an example for making minestrone, using leftovers:
You can substitute to your heart's content.
Here is a totally different version, so you can see how flexible it is:
And here is a more "authentic" version, if there is such a thing: