Just to get started, and see if you take to it, I would highly recommend Rodney Yee's Yoga for Beginners videos. I used to have a few of his DVDs but these days they're available in various places online. Start with "A.M. Yoga". (there's a PM Yoga, too, of course ...)
Yee is definitely not too New Agey, and he's a guy guy! Those vids are pretty gentle, which is definitely the place to start, and I find him one of the few non-annoying presenters of yoga videos.
I would probably suggest you try one of those before trying a class, just to get a feel for what it's about.
Classes tend to come in a great multitude of types these days. You would just have to look what's around in your area.
But be aware that, as gentle as yoga looks, you can easily trigger PEM with even quite a short session. Yoga works the body quietly, without impact, but steadily. It's easy to do too much if you have low exertion thresholds.
I've been doing yoga for more than 30 years, since adolescence. Never a big deal for me, always a thing to do when I feel like it (or, these days, when I'm up to it). I can only do it in small doses since getting ill. For me it's just something I work quietly into my life as and when I can, in little bits and pieces. And I love it.
Do try the Rodney Yee. He's a cool guy, and very likeable. That particular vid I mentioned is about 20 minutes and will give you a nice sense of both the relaxation and exercise potentials of yoga.
p.s. don't worry too much about all the different, exotic sounding types of Yoga. Most variants are based on the same core principles and elements. And most of what you're likely to find will be based on one traditional form, Hatha Yoga. Frankly, in 30 + years, I've never bothered learning much about all that or learning all the Sanskrit words .... some people love all that, but it's not compulsory!
p.p.s. there are certain yoga postures that I've learnt the hard way are guaranteed PEM triggers for me, and i avoid them. One of them is one of the classics, the 'downward facing dog', which I used to do with ease. Go slow, go gentle.