Most of what I thread is much smaller than what you would use for learning. And the advice given herein on this site is on point. I wanted to bring up a couple of points that might be useful to a novice. Once you have a good understanding of threading, much of the details will become second nature.
Theoretical threading of standard 60 degree threads is called a "V Sharp" thread where the OD is exactly the diameter of what you are working toward. And the bottom of the thread is a sharp "V" or 30 degree angle. But as is often said in many fields, "in theory, theory and practice is the same, but in practice they are not."
In Practice, the tooling will "dull" a whisker so that the V Sharp is no longer sharp. This is outlined in Machinery's Handbook, which has editions going back to 1916. I don't know the current standards for threading, they have changed several times over the years. But the final touch up of threads involves taking a whisker off the OD after the threading pass(es). And the bottom of the thread is actually a slightly rounded form for the same reason. In production, tooling will dull after a while.
In practice, the slightly undersized OD is a practical solution for the outside of the thread. When I cut a 32 TPI thread on a 3/16 rod, I start at 3/16 inch and cut to a sharp profile. Then following the threading cut I touch up the edge with a whetstone to the point that the sharp edges are gone. Essentially duplicating the "standard" given for a Unified Thread. Unified Threads are a post WW2 phenomenum. where, among other things, Whitworth 55 degree threads were reconciled with 60 degree threads. I only understand about 10 percent of all that, it's a deep subject.
The bottom or inside of a thread is a function of the nose radius of the particular tool used. It is normal for the novice to use carbide tooling to learn. Either brazed or insert types. If you look closely at the specifications for a particular insert, there is a given size for nose radius. When grinding HSS tooling, this is less of an issue. For a threading tool, the target for grinding is a sharp point. But grinding tools is as much an art as a science.
The point is that a carbide insert for a "large" thread, say 10 TPI, is in no way suitable for a smaller thread of 56 TPI. It simply doesn't cut deep enough. Leaving the bottom of the thread too shallow or rounded. 56 TPI requires a much smaller nose radius. As grinding tools is an artform, so too is threading. There are many details to be learned, but the final parameter is "touch". Just how much to make that last pass where you don't adjust any deeper, just make another pass to smooth up the surface. That's the art part of threading. I highly recommend acquiring a copy of Machinery's Handbook. Which edition you acquire is as much a matter of what you will be doing. I have several copies, including a 1942 version and a 2005(?) version for when I need to see what the current practices are.