There are so many types - and in the west newer variations appearing - that just listing each would probably be worthy of a research grant [if you aren't paying me for the research then I am not about to do create that list!] :)
Hatha yoga is often seen as a great place to start, but don't let that fool you that it is only 'good for beginners', it's good for everyone.
Vinyasa (flow) is becoming the style seen more commonly in gyms as it appeals to the people that 'like to get a sweat on' [But that's a bad way to think of it, for one thing, you can still 'get a sweat on' in. a hatha class and with other styles too...]
So when it comes to decide which class is for you one of the factors is the STYLE of yoga. No, I am not referring to the baggy pants or the lycra leggings, but the the style of the class.
Another consideration to factor in is your current physical limitations. If you know you struggle just to get up off the floor, then a flowing class isn't the best place to start.
As well as the style of yoga, consider the Instructor/Teacher's teaching style. It could be that a particular instructor likes to try to inject humour - you may not appreciate that or find the person in any way funny.
Do you want to be physically challenged in a class?
Are you looking for mindfulness and relaxation?
Do you like/dislike music playing in the class?
Do you want to learn sanskrit, or happy just working with the english names for the poses?
Do you want a general or a specialist type of practise?
How do you know which yoga style will work for you?
Try one. If you like it great, if not ask yourself why?
If it was the yoga-style, music, humour, etc. then consider trying a different yoga-style.
Was it perhaps the teaching style though? In which case you might actually like that style of yoga if you went to a class with a different teacher?