When I used to run my own business and someone would call about coming to work with my I always advised them to start with one class, rather than buying the 6 class ticket I sold. My reasoning was that I knew I was a good teacher, but there are many good teachers. (i.e. it is a necessary, but not sufficient condition) The question was was I the right teacher for that person at that time in their life. So the first thing I would suggest is: if you took a class and did not care for it, try a few others. Styles vary greatly, and even within (and definitely between) styles teachers vary greatly. There is not one teacher, or one style that is better than any other for everyone.
The history of yoga, of how the different schools, and parts of the practice arose is interesting, and MUCH more complex than the usualy one or two paragraphs everyone recites. If you are interested the book Yoga Body by Singelton gives an excellent in depth account of the practice of asana in its historical context. But its antiquity is a seperate issue from its validity, and if we assume you are ready to do yoga and just want to figure out what is available now knowing the history is not required.
If you have a specific physical condition or injury I would suggest first consulting your medical practitioner for some advice and guidelines. Then I would suggest looking for someone with real experience in that area. Do not just stop with someone saying "I can teach anything, I am awesome".... look at the credentials, or get referrals. With some students this is particularly important. If you are pregnant and know the ACOG guidelines and have done yoga for a long time you could probably do a general class and modify, but going to a prenatal class will provide a deeper and more focused experience, if it is possible for you to find one taught by a careful, experienced teacher. Child focused classes are also great.
If you are relatively new to yoga try this: Compute the longest drive/trip you do at least a couple of times a week. With your house as the center draw a circle around that point, with a radius equal to that number. Then search for locations within that circle. A person who has done yoga a long time within a particular school may be motivated to drive to a particular place, but it is probably easier to build a new habit if you stay in your comfort zone. Plot a line from your work to home and look particularly for things close to that line. If it is easy to get there you are more likely to go.
Yoga is taught in yoga studios, in health clubs, in senior centers, on the beach, in parks, at retreats, in apartment building common areas, in schools, in universities.... Is there a best place? I do not think so. I think each option has advantages, and if it is easy to get there, you like the teachers, it is within your budget,..... try it out. One advantage of a stand alone yoga studio is that the owner typically is a yogi or yogini in their own right, and will be very good at knowing how to bring in other teachers with excellent training. Another is that a dedicated space typically is designed for the activity: heat, light, props, etc. One advantage of a health club is that you can get the yoga along with other activities, and though yoga does many things it is not (from what I can see in the research) going to provide as much aerobic training. And cross training is excellent to vary the stress on the body to avoid injury. Yoga training is very expensive, so very well trained people will tend to gravitate to pay per person sites because otherwise they could not afford to do what they need to do to continue to be the teachers they are..... however, plenty of experienced teachers will do classes in a club to get membership privleges, or because they do other work there as well, or because they really like the facility, or because they believe in the mission. I do a lot of work in places that offer low cost classes because I care deeply that this be available to everyone. I love beginners to walk into my class and let me help them find places in themselves they have never looked. What a huge gift it is to me.
I do not want to give a long history of styles and schools. You can google that and get hundreds of explanations. I just want to give a couple of suggestions.
Not quite 15 years ago The Yoga Alliance was formed to provide a single place to gather information about yoga teachers, schools, and trainings. When a yoga teacher applies to be on the registry they get a designation based on training and experience. The standards are the same for all schools, so it is a good place to start. To look at the various levels you can go to yogaalliance.com. You can also find schools and teachers by location. Are teachers who are not on the registry not good? Absolutely not, (I was looking recently for a teacher I trained with named David Swenson and could not find him there, and he is one of the greatest teachers of his form today. He trained in Ashtanga yoga with Sri. K Patthabi Jois himself!) but if they are there you have a starting point that they have a certain amount of training.
If you are very interested in allignment you might want to look for an Iyangar teacher. Iyanger training is particularly rigorous. If a person has an official Iyanger certification they have done many years of training to get there.
If you like a physically demanding practice there are a number of styles that might speak to you. Vinyasa yoga comes in many varieties, but tend to be stronger practices. You usually need to be able to be on your wrists, though I have worked with people in this type of practice with lots of different variations. Ashtanga yoga per se (and a few other styles), unlike some forms of vinyasa practice, have a defined series of postures that are practiced in a set order. Some people find this great for focus, some do not.
You might want to read a bit about various styles before you begin: Iyangar, Kripalu, Bikram,Viniyoga, Ashtanga, Kundalini, Sivananda all have their own particular foci. But you may find a teacher you love in a style that you did not think would reach you,... so be open to possibilities.
And, of course, we have not talked about the meditation or lifestyle aspect of doing yoga, but this seems like enough to start!