As with anything audio the answer is it depends. What equipment is at our disposal? How much time do we have to prepare? Etc. What I will say is there are no “rules” in audio, just guidelines. Try to learn what the rule was attempting to accomplish and see if it’s applicable for you. The 3:1 rule is so rarely applicable for me in the live and broadcast world that I never even consider it. The moment you put more than 2 microphones in a space the 3:1 is no longer applicable.
What I usually have remind people of is that the conductor should be doing most of the mixing for you and all you need to do is capture it. A stereo configuration either above the conductor’s head, or if it’s being filmed, directly in front of their music stand usually gets you 90% of what you need. That stereo configuration could be XY, ORTF, A-B, or binaural depending on space and budget. I never run a decca tree, I’ve always gotten better results out of a simple spaced pair. I will however run a williams star or standard star.
If possible I would do an area mic for each section of the orchestra and choir. For the choir specifically pay very close attention to the polar pickup pattern of your mics and use that to fight the inverse square law. You will be micing closer with the choir than the orchestra and as a result the inverse square law will play more into the micing results. If you can, position the orchestra in the null of the choir mics, that will help in the final mix.
As for style of mics (condenser, cardioid, whatever) that all depends on your room. Condensers are great, but dynamics work just fine. I tend to use condensers as I like the subtleties they produce, but if you find you are getting too much noise bleed or room echo, especially in the choir section, go dynamic. As for pickup patterns I can’t tell you what kind to get as that’s way to specific to your room and layout, if you’re unsure a cardioid is always a safe bet.