There's different schools of thought on this. I 100% cater the Spire because I keep that resource completely separate from my tournament resources, where I always fight. I always have plenty of goods for catering there and it's just a matter of making sure I have enough coins, supplies and orcs for the job.
I find the separation much more simple, but plenty of people will tell you they fight through both, or a different combination.
I don't think there's any pattern with the spirits. Entirely random. There's plenty of logic involved in solving them though, plus some guesswork.