People start yoga for many reasons. They may want to increase their levels of health, fitness, and flexibility. Or improve their muscle tone. Reducing levels of stress and anxiety are also high on the list, as is personal development, and the desire to follow a more spiritual path. Some may have a particular medical condition or health problem they want to address.
One's reason for starting yoga may have a bearing on both the type of yoga that makes a 'best fit', as well as the particular teacher chosen within a yoga discipline. Whilst the different types of yoga obviously suit some aims better than others, the teacher you practice with will also make a difference to achieving what you want with yoga. Or not.
Foe example, if you have a specific medical condition, it would be better to informally interview prospective yoga teachers beforehand. First, to find out which classes might be suitable, and to see whether that teacher has a real grasp of what the condition or problem implies for a yoga practice. Some people, whether they are yoga teachers or not, have a more rigid outlook, and may not be able to appreciate that a flexible approach in such circumstances is important. Or, they may not have sufficient training or experience. Perhaps they are even too busy to be available in a more personal way.
When choosing a yoga teacher, it's important to use your intuition. And to understand that we, as individuals, may not find our needs met by a class even if others do. Some teachers are more nurturing than others, some are more focused on the spiritual aspects of yoga (which may or may not align with our own spiritual outlook). Some perform adjustments - which is where a teacher will use their bodyweight to help you go further into a position - without really finding out whether a person has any injuries. And some simply do it too overzealously. A student in that situation may feel that the 'teacher knows best'. But it's important to listen to your own body, and understand that not all yoga training is equal. And, not all teachers are equal, in all areas, either.
Some other things to consider when choosing a yoga teacher are:
Are they dogmatic? Do they push a certain philosophical or spiritual viewpoint? Is there a subtle (or not so subtle) manipulation that implies that without their 'guru', your spiritual evolution is on shaky ground. In fact, do they suggest that you 'need' a guru (their guru) as a 'guide' in matters of spirituality because your own connection to Source-God isn't good enough. In other words, are they suggesting you place your power outside of yourself, or do they reiterate that you in fact are your own guide, and can get their quite well under your own steam.
Are they (or the prominent representatives of their yoga discipline) overly concerned with money, fame, power, the size of their organization, or their degree of influence? If they (the organization) certify yoga teachers, how long do the teachers have to train for? What are they trained in and what aren't they taught about?
How well does the teacher embody the basic spiritual qualities of compassion, kindness, peace, joy, and equanimity? Whilst we are all beings at various stages of the journey, it helps to look at a teacher's character, and ethics. No-one needs to be perfect, but what qualities, of themselves, are they bringing to class.