The ones centered on Rincewind aren't as good as the others, other than that it doesn't much matter.
I'd just start with "Guards, Guards".

Publication order is probably fine, though it takes a few books for him to settle into his general story structure. It's not the only way, and unless you're going to sprint through them in relatively quick succession it's probably not the best way, as you may get lost in some of the focused character development.

This is a bit of an open question. Most of the books center around one or another subgroup of characters (City Watch, the wizards, the witches, Death, etc.), although there's some overlap. The way I've been going through seems to be roughly the agreed upon "best" way: choose one of these sub-groups and read all the books that center around them in order, then move on to another.

Those sub-series are relatively self-contained, so I think you get more from exploring a theme from beginning to end than jumping from theme to theme. There are several tie-ins, but I don't think they're substantial enough to agonize over missing context.

Personally, I'd either start with Guards! Guards! or Going Postal, as they're the beginnings of the more grounded sub-series and give you a good foundation of the world in general, and Ankh-Morpork in particular. But as long as you're not skipping ahead in a sub-series, you should be fine.

The way I came into it was reading them all in order. I’m told this is not the best way and that there are flow charts.

But I like this way because I got to see how Sir Pterry evolved as an author and I got to see them in somewhat disjointed order rather than going through individual characters or arcs. It felt more like a fleshed out universe that way, and I love great universe building.