Cool. Hatha is the basic yoga style, everything develops from it, so it's the right place to start. It's usually not the fastest or bendiest (but also not the most scary rigorous everything-must-be-perfect, stand still till your legs ache, which is Iyengar, can you tell I don't love it? But I know nice people who do). So it'll depend on your teacher what he/she makes of the class, up to a point. But it's a very good sign that you know what kind of yoga it is. Crappy teachers often just say 'yoga'.

My experience of yoga class when I first started (fat, introverted and on a downswing from anxiety into mild depression, so I wasn't in a good place to wear lycra in front of strangers) is that although you need to find a teacher you click with, they are usually very nice as people. And most people who go to yoga class (especially to try it out the first time) are either stiff/unfit and worried about being the worst in the class or have some minor mental health thing like stress or anxiety that drove them there. I relaxed *so much* when I realised half of us really were there because pills weren't working well and nor was RL.

So I'll stop now. But I hope yoga works for you too :-)