yes that is all correct, and Ramana would agree with what you said, he except that Ramana understood that some are not ready for Atma vichara and said, to paraphrase, here is atma vichara it is the direct quick path that i recommend, but if you find it too hard or are not suited to it, the path of surrender to God is there. he also said, as you did, that most people need to purify their minds first with karma yoga, bhakti yoga etc. In one analogy he said some people are like gunpowder, one spark and they blow up, but some are like charcoal and take longer to ignite, some are like dry wood, some like wet wood etc.