In picking a latin program, you do have a choice in the type of Latin to study - between "classical latin" or "ecclesiastical/Christian latin." However, to clarify, they are but one language. They differ primarily in pronunciation; sometimes word order is a bit different but vocabulary is 95% the same.
A commonly used example of the difference in pronunciation between the two styles: Caesar's famous "Veni,vedi,vici" (I came, I saw, I conquered) in classical latin would be "Way-nee, wee-dee, wee-kee" versus Christian latin "Vay-nee, vee-dee, vee-chee." But its still written "Veni" and the word is the same whether you use Christian or classical latin.
Classical latin is considered more "flowery" and stylistic - it was the latin of the elite at the time, used for political oratory or epic poetry recitation, and used for a relatively short span before it fell out of favor. Christian latin, though, was more blunt and "to the point;" it became widely used in the first thousand years A.D. It is easier to understand with more predictable grammar, less flowery. There are many original non-religious works that were written in this style, it was not limited to church writings, and yes, you can use it for 'real latin reading.' All the same latin, same case endings, same declensions. Yet I can see having a much more difficult time translating the Aenid (much older, flowery work, complicated syntax), versus, say, a New Testament Biblical text from the latin, no matter what style of latin you have learned.
I found this quote interesting, from an article by Leigh Lowe of Memoria Press, "Latin was the international language of Christians for over a thousand years. To exclude this in favor of focusing solely on Roman Latin content is a common mistake. Acknowledging both Latin's Christian and classical heritage offers the more historically accurate cultural background for the language." She makes a good point. Of course its only her biased opinion, but I see value in it. I don't believe Christian latin should be ignored. Consider that many colleges offer a latin program incorporating both classical and Christian latin. At my friend's daughter's college, they are required to do two years of Christian followed by a year of classical latin. My friend's daughter eloquently says, "The difference can be compared to American English versus British English, and either approach can still read Tolkien". There are differences, yes, but you can still read original works in both.
There is a misconception that Christian latin programs somehow ignore Roman history. Not so. Even with a Christian latin program, there is usually an emphasis on Roman history. With Christian latin, however, you have the addition of classic Christian hymns we still hear today (like Adeste Fideles - O Come All Ye Faithful - a common Christmas hymn), and classic Christian prayers, like the Our Father - which you won't generally find in strictly classical latin programs - and which can be used or not in your study, as you like. That alone may rule one program out over another, based on your core belief system. If, however, the Bible is part of your core, I would strongly consider a Christian latin program.
Another misconception is that only classical latin will give you a foundation in medical terminology. Not so. In studying Christian latin, you get the same understanding of science/medical terminology as you do with classical. They are not mutually exclusive, and that is one of the big arguments for ANY style of latin - that it is the language of science and medicine. So you don't 'give that up' if you do one style versus the other. Truth be told, Greek was the language of medicine up to the first century A.D., even for the Romans. Greek terms then began to be "latinized." For example, the original Greek and Arabic medical works were translated into the common latin in the late 1400s and subsequently (think Galen, and De Medicina), in the common latin of the day.
All that aside, I think something to keep in mind when choosing programs is the level your students are at, and to meet them there with something that will ... drumroll .... truly inspire! Or at least create some interest! Ask yourself:
Does your child excel in logical thought and solving brain puzzles?
Perhaps a translation-approach will be the hook for him. While beginners will find it difficult to jump right into latin translation (whole-to-parts approach) without doing the hard work of grammar first, maybe this would suit your child. However, at some point the grammar has to be learned. Jumping right into translation might be completely overwhelming and kill any interest there might have been. Consider, for example, that Wheelock Latin was written for college level. So for beginners, a program that progresses parts-to-whole is usually better. That being said, if you have an older child who has good use of logical facilities, than maybe a translation-based program will be the hook - the puzzle for him to solve.
Does your child love music? Especially music history?
Latin truly helped shape the style of music in the first 1000 yrs A.D. Think Gregorian chant. If there is a strong love of classical music, maybe this is the hook for your child to learn latin chants, which represent the Christian culture of the time, and then develop a greater interest in the language.
Does your child delight in words and language and spelling in general?
You may consider a program that uses a "roots" approach instead of grammar approach. While teaching latin roots and the english words that have derived from them is very different than learning the grammar and sentence structure of a language, a "roots" approach might be the gentle hook that gets your child interested in latin itself, and inspires him to move into it more deeply. My oldest daughter really inhaled all the latin and greek vocabulary programs she could find! My son did not :)
And finally, if one program "fails," and you still want to pursue another, it is entirely possible that you may need to start back at square one because the approach, scope, and sequence to teaching latin differs so greatly among programs, be it going from one classical program to another, or from one Christian program to another, or crossing from Christian to classical. Too bad it has to be so complicated!
I have recommended them before and I would suggest for further reading: