Hello Apex! Good to see someone showing interest in the martial arts. Before you sign your daughter or yourself up for anything, try out a class or two. Most martial arts studios will let you try a class to see if you like it. The best way to choose a school is to look at what you want to get out of the class. Most people have physical fitness in mind when they are looking for a martial art. A good martial arts school will offer more than just physical training, i.e. disipline, ect. One thing to watch out for is the student to instructor ratio. If you have one instructor teaching 20 people, it's tough to ask questions or get corrected on techniques.
As for the martial arts you listed: Tae Kwon Do is the most common of them all. A lot of people will join Tae Kwon Do because it's what they always hear of when someone talks about martial arts. Akido is a strictly defensive art that focuses on leverage to defeat an opponent. As for the martial art that they taught ninjas, that is ninjitsu. Jujitsu is different, although I am not very familiar with it. Muay Thai is Thai boxing. That's a bit more hardcore. They use their shins and elbows a lot in combat, so you spend a lot of time beating on your shins to condition them so it doesn't hurt when you strike with them. May not be something your 5 year old would enjoy!
If by Portland, you mean Portland, OR there's a school there that teaches the same martial art I am practicing now. It's called Hwa Rang Do. It's a Korean martial art dating back 1800 years. Very rich tradition and a very complete system. If you would like to look at the school before you go in, here's the website address:
http://www.hwarangdo-pdx.com/
I would encourage you to at least go to the Hwa Rang Do school and watch a class. You would most likely start out in a Tae Soo Do class, which is a bit different than Hwa Rang Do. It's geared for beginners without much prior martial arts experience. Think of it as the undergraduate program to Hwa Rang Do. If you have further questions about Hwa Rang Do, feel free to ask here, or you can also Private Message me if you wish. Good luck in your search!