The organization I want to join

The School Club I Want to Join

"Organization" generally refers to an official group that works toward a specific goal. A school club isn't really an organization. The Red Cross is an example of a large organization

The school club I most want to join the most is the computer club.

This sounds a little unnatural because you would normally give some context for this information before writing this.

To get a desirable job opportunity in the future, I need to computer skills in programs such as Microsoft Powerpoint, Word, and Excel for our future job.

Powerpoint, Word, and Excel aren't actually skills, so you would say that you have skills "in" or "with" those programs. The word "skills" can be difficult to use correctly because its meaning changes slightly depending on what it is describing.

Second, for my education.

I’m a student of computer science major, so I’m really interested in computers in general.

You can end this sentence in a few different ways, but this has the broadest meaning.

By joining the computer club, I can learn about computers all day long.

You should refer to "computers" as a plural, instead of a singular noun when you talk about a class of object such as computers. The singular will usually make the reader think that you are talking about one particular computer.

So I can learn about programming methods to improve my education.

It sounds like this could have been part of the last sentence, but I left it as a separate sentence.

That is why the club I most want to join the most is the computer club.

I put "club" instead of "school club" because the reader already knows what kind of club you are talking about.