Hi Jon,
I have been practicing yoga seriously for a little more than five years (10 before that off and on) and I may be able to shed some light on the various styles for you.
Most of the styles you've asked about incorporate the same or similar asanas with common goals. The biggest differences usually come in the instructor. I would say that it's more important to search for an experienced instructor and then for a specific style. My personal practice developed a great deal when I started studying with a very talented instructor in a style that I had not even been interested in.
When you're looking for an instructor keep in mind that yoga has become quite a fad these days and that has resulted in many instructors popping up without much practical experience. It is experience that makes a good instructor, not necessarily training. So, take your time looking around for an instructor that you feel comfortable with and who has been around for a while. Even when you do find that instructor that clicks with you, I would recommend visiting other instructor's classes every once in a while to get a different perspective on your practice.
You commented about the cost of a yoga studio vs. the Y. If money is an issue I'd do the following. Find a good instructor regardless of where they teach. Attend as many classes with them as you can afford and the rest of the time practice at home. You can use what you learn in class to guide your home practice. In the end, the best instruction comes from being able to listen to your body and learn/teach yourself.
Wherever you practice, remember that consistency is the key. You're better off practicing at home for fifteen minutes a day, every day, than going to a class once every couple of weeks. If you can only do twice a week, fine. Just do what you can. When I first started I had only planned on going once a week, but I felt so good after doing yoga that it quickly became a daily practice for me.
As for the disciplines... I'm an Ashtanga and Bikram guy myself.
As you know, Bikram is in a hot room. You either love it or hate it, but the benefits of the heat are great. Unfortunately, because the heat is very important to this style it is difficult to practice at home. The focus is more on effort than form as Bikram teaches it, but instructors will vary. The cardio benefits can be great, especially as you develop and are able to focus more on your breathing. I go to Bikram classes when I'm really tight and need to open up.
Ashtanga is a great workout in every way. This is my favorite style and I practice it daily. The cardio benefits are amazing and the breathing used during practice will definitely help your freediving. Don't let your ego get in the way though. Many ashtanga postures can be very challenging and if you push too hard you can injur yourself. This is the case with all styles, but I'm speaking from experience regarding ashtanga. One of the benefits that I like about this style is that it gives you a great upper body workout which many other styles don't.
Kundalini is great if you want to unleash some of those natural "drugs" within your body. This style focuses on moving the energy in your body around and releasing it in different ways. It's something you should definitely try at some point, but I doubt it's what you are looking for right now.
Vinyasa is derived from, and will have many similarities to Ashtanga, but I have little experience with it specifically.
Iyengar, depending on your instructor, can be very prop based, but I have little experience with it.
Forrest, no experience with it at all.
If you're going to do some home practice, which I'd recommend, then there are a couple of books/videos you may want to pick up. David Swenson and Richard Freeman are two of the most recognized and accomplished Ashtanga instructors in the world. Both have books and videos and you won't go wrong with either.
David has a video called Ashtanga Short Forms which takes the entire primary series (1.5 hrs) and breaks it down into shorter more accessible sessions of 15 min., 30 min., and 45 min.. This is great when you're just beginning until you can work up to the entire primary series. It's also good for home practice. I'm sure that Richard has a similar video out.
David also has a spiral bound book that goes into the details of every asana in the various Ashtanga series'. It's difficult to use the book as a guide when you're just beginning, but it's an excellent resource as you develop and want to learn more. I use this for my Mysore practice all of the time. Mysore is a personal practice done in the presence of an instructor who provides personal instruction as needed as you progress through your practice.
I hope that this hasn't been too long winded of an explanation. Of course all of this is simply my opinion and others may differ, but one thing you'll realize quickly as your practice develops is that yoga can be a very personal pursuit and everyone's experience will differ.
Good luck.
Jason Billows
Ottawa, Canada