I like to suggest a different path. An ornament in early music was not a choice, it was really the part of that particular musical style. It's not like you could perform a piece without ornaments and it would sound fine without them. The ornaments were one of the basic elements that made that style real.
So it appears to me we should learn to play the ornaments right from the start. This of course is a tricky task for many people. But the real reason people can't execute ornaments well is not because they don't know how they should sound (it's easy, just click here for the famous table from the Clavierbuchlein for W.F.Bach which lists all the main ornaments that J.S.Bach (and many French Baroque composers) used.
The real reason is that many people have a weak finger technique. When they start learning a piece and want to add a trill, often it becomes a mess. They struggle playing it the right way, even in a slow tempo. Especially in a slow tempo.
What I really recommend in such situation is to work on improving your finger technique. Those technical exercises little by little will begin to pay off in the end. Of course, you could strengthen your fingers and playing from the great collections, such as Two-Part Inventions and Three-Part Sinfonias by Bach.
Too many people learn one or two of these little gems, become bored and move on to something else. But what if you could master all 30 of them? That's what Bach would recommend to his eldest son, Wilhelm Friedemann - we know that for sure (he included them in a collection specifically designed for his development - not one or two but all of them). If you could do that - your finger technique would become really solid and you will not have any trouble with playing ornaments (because these pieces are full of them).
All of this has to be done very slowly and without haste. Treat the ornaments as part of the piece and learn them right away. Working in separate voices and in short fragments repeatedly is a key here.
Of course, there are many stylistic differences in terms of how you would execute the trills in pieces from different schools of organ composition (Spanish, Italian, French, English, South German etc. - check out Historical Organ Techniques and Repertoire series from Wayne Leupold Editions if you are really serious).
As in everything with organ music, the slower you practice your ornaments, the faster you master them.