The size of tooling will depend on the lathe in use.
No point in getting Carbide tipped tools for a lathe made 50 or more years ago. It is unlikely to be powerful, fast or rigid enough really to do them justice.
Too big and they will be above centre height, so useless, for your machine.
Too small and they will be flexible and possibly cause problems. Plus you will need lots of shims to set them to centre height.
You will learn the basics by grinding HSS tools. (In any case, they function slightly differently from carbide tips ) Carbide tips were developed for Industrial machines specifically to remove metal, sometime quite exotic or hard, fast.
Model Engineer are not usually on piecework!
Reading will give the basic knowledge, which you can then put to practical use, because you have a better understanding of what you are doing.
You could waste a lot of time and good metal trying to grind a tool when 30 minutes with a book could tell you haw to get it somewhere near right, first time!
As an Apprentice, we had face to face instruction, with regular Lectures with handouts, in addition to plenty of workshop time to put it into practice. In this way, we had an understanding of what we were doing, what was happening, and why.
I am not a skilled machine, only had the first year basic training. The machinists spent four or five years learning their trade. My turning instructor could work, with a 6" rule, to within a few thou of how I could with a micrometer!
You can grind a drill, freehand, but unless you understand how to grind it, it will not not cut well, possibly not at all, or even anywhere near accurately. The same goes for a lathe or any other tool..
Howard