I hope that other knowledgable people will join in with their expertise to make this thread sort of a one stop source for learning about system component compatibility
The most important ingredient is common sense. Unfortunately, newcomers to the hobby mostly choose gear to impress themselves and others - an item must distinguish itself first and foremost based on aesthetics, testimonials, and sticker price (especially important is that an uninitiated should utter "wow" upon simply seeing the item). Typical manifestation is the music loving wealthy medical doctor whose kids have just finished college and now finds his/herself with disposable income and who one day walks into a high end store and is bowled over by the sound.
The false assumption is that price/aesthetics will indeed overcome all other common sense factors such as speaker placement, room acoustics, equipment design and equipment compatibility. Typical manifestation of this logic is an emphasis on precious metals such as gold or silver or speakers with $10,000 of woodwork and veneer and $500 worth of drivers/parts.
The end result is disatisfaction and propagation of more audio myths about the performance of certain equipment, often the wrong piece of gear is singled out and blamed for the inevitably inadequate sound, or worse, the use of one poorly performing piece of equipment may result in the anecodotal extoling of the virtues of another poorly performing piece of equipment that together compensate for one another or for room/placement issues....and the merry-go-round begins. Of course, for some there is intense enjoyment from the merry-go-round itself and the thought of ever getting off would take all the fun out of the hobby.