Sorry but that is simply incorrect information!

Many people work in Japan without work visas or working holiday visas, you can work on any visa in Japan EXCEPT temporary visitor. It is just a matter of having correct permission. For example, a student can work if they have special permission with the student visa. However, to get such permission takes at least 3 months from when you start school, also you are much much more limited in work scale with the student visa.

You are free to do more different types of jobs with a Working Holiday visa, also the hours are more flexiable. Work permission with a student visas is highly restrictive in the type of work and the amount of hours allowed to be worked.

Also as mentioned, no school is going to sponsor a student visa unless you are committed to at least 1 full year of study and pay at least 6 months tuition up front. Most people who come to study for 3 months come as a temporary visitor.

So your course of action is learning towards getting a working holiday visa. Pretty much jobs depends on what you are qualified to do. Speak Japanese, are you a lawyer? My friend speaks japanese and has a law degree so works for an international company. No qualifications? Then well its harder, maybe part-time english instructor.

That income only from such part-time job would not be of course covered enough to tuition and daily living life including house rent etc. in Japan. For satisfactory study in Japan it is required that you'd have kept ample stocks or funds in advance.

Don't count on possible albeit income there. It is in the midst of the heavy recession there in Japan, as well as Britain except cheap unofficial English teacher.

You can't get any student visa for just 3month stay. Any school in Japan officially won't support you to apply the visa in accordance with the short term at all. Your financial reason has nothing to do with the rule.

Your any visa can't extend so easily like what you say right now in Japan. Actually any recruit of foreign student won't get any job in current Japan at ease.

Under working holiday visa, the best and easiest way would be English assistant teacher. Check the web site about JET program. You would be elisible to be ALT.

So your plan of going to Japan for 3 months and extending visa later does not work.

Besides, you are only allowed to have part-time job on student visa. And the time you can work is limited.

The government does not issue student visa if you don't have enough money to live and go to school in Japan without working.

Your only option will be working holiday visa.