I am (or was as currently not practising) first dan black belt in Seido Karate.

Just to answer your question re different types of martial arts.

Different martial arts developed in different Asian countries and/or regions within a country.
A lot have different emphasis on technique and their teachings.
For example judo is a style in which throwing or grappling your opponent to the ground is its main focus.
Karate is probably what most people think of as a martial art (punching and kicking).
Tai Chi is also a martial art- abet a slow, gentle almost dance like martial art.

You need to find one that suits you. I would probably run a mile if all I saw was men (and no kids or women) and they make you free fight (spar) as a beginner. I liked Seido because they don't allow you to spar until you are a green belt (6 levels up). I did karate from age 11 to 19 and felt it gave me confidence at a time I didn't feel it (along with glasses, braces etc) and I still have my certificate, gi, and belts which I look at with pride. However cycling is my new passion!