If you are not experienced with multi-threading you should probably not start with TThread, as it is but a thin layer over native threading. I consider it also to be a little rough around the edges; it has not evolved a lot since the introduction with Delphi 2, mostly changes to allow for Linux compatibility in the Kylix time frame, and to correct the more obvious defects (like fixing the broken MREW class, and finally deprecating Suspend() and Resume() in the latest Delphi version).
Using a simple thread wrapper class basically also causes the developer to focus on a level that is much too low. To make proper use of multiple CPU cores a focus on tasks instead of threads is better, because the partitioning of work with threads does not adapt well to changing requirements and environments – depending on the hardware and the other software running in parallel the optimum number of threads may vary greatly, even at different times on the same system. A library that you pass only chunks of work to, and which schedules them automatically to make best use of the available resources helps a lot in this regard.
AsyncCalls is a good first step to introduce threads into an application. If you have several areas in your program where a number of time-consuming steps need to be performed that are independent of each other, then you can simply execute them asynchronously by passing each of them to AsyncCalls. Even when you have only one such time-consuming action you can execute it asynchronously and simply show a progress UI in the VCL thread, optionally allowing for cancelling the action.
AsyncCalls is IMO not so good for background workers that stay around during the whole program runtime, and it may be impossible to use when some of the objects in your program have thread affinity (like database connections or OLE objects that may have a requirement that all calls happen in the same thread).
What you also need to be aware of is that these asynchronous actions are not of the “fire-and-forget” kind. Every overloaded AsyncCall() function returns an IAsyncCall interface pointer that you may need to keep a reference to if you want to avoid blocking. If you don’t keep a reference, then the moment the ref count reaches zero the interface will be freed, which will cause the thread releasing the interface to wait for the asynchronous call to complete. This is something that you might see while debugging, when exiting the method that created the IAsyncCall may take a mysterious amount of time.
OTL is in my opinion the most versatile of your three options, and I would use it without a second thought. It can do everything TThread and AsyncCalls can do, plus much more. It has a sound design, which is high-level enough both to make life for the user easy, and to let a port to a Unixy system (while keeping most of the interface intact) look at least possible, if not easy. In the last months it has also started to acquire some high-level constructs for parallel work, highly recommended.
OTL has a few dozen samples too, which is important to get started. AsyncCalls has nothing but a few lines in comments, but then it is easy enough to understand due to its limited functionality (it does only one thing, but it does it well). TThread has only one sample, which hasn’t really changed in 14 years and is mostly an example of how not to do things.
Whichever of the options you choose, no library will eliminate the need to understand threading basics. Having read a good book on these is a prerequisite to any successful coding. Proper locking for example is a requirement with all of them.