Hank - you ask a good question but unfortunately there isn't a simple answer. There is information out there from various places but it is all incomplete because the options are almost unlimited. What i mean is each turning tool can be used to do many different cuts and each cut can be done with multiple tools. When you add in how many ways you can shape and reshape the tools the list of combinations becomes endless.
Let's say you want to make a candle holder from a 2x2x8 blanks. There are many different tools you could use and each of them can complete the job start to finish. Roughing gouge, Spindle gouge, detail gouge, bowl gouge and skew are all good tools to use. Each can do the job start to finish.
Want to roll a bead? It can be done with a detail gouge, skew, bowl gouge.
Want to turn a bowl? A bowl gouge or heavy scraper can do it.
There are a couple NEVER DO THIS situations. The main one is turning a bowl. Never use a skew or a roughing gouge to turn a bowl.
As far as tool shapes go there are so many possibilities. The real trick is to find the one that works for you. For example bowl gouges can have flutes that are V, U or parabolic. Different people, even professional Turners, will make arguments for why one is better then the other for the same cut but they disagree on which one is best. Then there is the bevel angle anywhere from 40* to 65*. Then there's the shape of the grind, often referred to as a fingernail or swept back grind. How far back it should go and how you should set your jig is different Turner to Turner. Or you can free hand sharpen. Then there is the 'standard' or flat across grind used on many 'bottom feeder' or 'finishing' bowl gouges. Bevel angle is often anywhere from 50* to 70*.
As you can see from the brief examples I have given, the possibilities are endless. I have experimented with different combinations on all my tools and also by using tools that belong to other Turners. I have settled on tools and grinds that work for me but for some tools I have multiple tools with different grinds. For example I have 5 bowl gouges, each with a different grind. On the other hand I have 3 skews with identical grinds because that is the only grind that seems to work for me.
The only way to know what works for you is to experiment. Once you find what works for you then you need to duplicate that each time you sharpen. I've given turning lessons to many people. Most have never turned before. When they have difficulty with a particular cut I give them a different tool to use for the same cut. That will often make a big difference.