What is a good dance style to learn for a beginner adult?

I haven’t ever taken dance lessons in my life. However, I started watching So You Think You Can Dance a few years back and have become addicted to watching dance. Now I want to take some classes so that I can go dancing with my wife.

I would like to learn how to do dances like the Fox Trot and the Waltz. Is that too hard to learn?

Also, where do people go to dance like this? I wouldn’t want to dance formal dances at weddings because I don’t want to be one of those dorky people who get all serious and try to use their dance lessons to look cool and end up crowding out everyone else that is slow dancing.

Also, I am not fond of swing dancing.

Any tips?